Ah, that's a shame. I was hoping you could help me with a maths problem.
If you give someone 45 billion somethings, but you don't actually have the 45 billion somethings to give them then how many days can you stay in office?
If you believe in modern monetary theory and are the creators of the somethings, then there are no difficulties
If you don’t , then if you have the ability to borrow the somethings and use them to create the conditions where more will be returned than borrowed (plus interest) then again it’s fine.
Vertigo, Although it has passed into rof lore, I was quite correct on that thread as several posters at the time noted, until they were bullied into changing their minds
Not a specific problem chambers, just creating to ‘grasp’ likelihood calculations on binomial distributions. (The conceptual difference between the term of art ‘likelihood’ and what most people would consider ‘probability’. Sorted now.
Iirc the X axis was and Y axis was growth rate. You missed the fact that the Y axis was growth rate and were claiming this wasn't exponential (i.e. as bad as others were claiming). The line was straight and I think slightly upward sloping so technically it wasn't exponential but super-exponential (i.e. worse!).
It says I can’t access it. I didn’t do anything to it. Why wouldn’t I have done it ages ago if that was the case? If you recall it’s been bumped many times.
Either way I hope this ChatGPT4 response helps with your degree. Good luck.
If X axis is linear time ,Y axis is growth rate and the series shows a horizontal line, is this exponential growth
Yes, if you're plotting growth rate (specifically, the rate of change of a quantity) on the Y-axis against time on the X-axis, and the plot shows a horizontal line, this indicates that the growth rate is constant over time. In the context of functions or series, a constant growth rate typically signifies exponential growth.
To clarify, for an exponentially growing function, the formula is often given as \(f(t) = a \cdot e^{rt}\), where:
- \(a\) is the initial value,
- \(e\) is the base of the natural logarithm,
- \(r\) is the growth rate (a constant),
- \(t\) is time.
The derivative of this function, \(f'(t) = a \cdot r \cdot e^{rt}\), shows that the rate of change (growth rate) of the function is directly proportional to the function itself. The constant \(r\) in the exponential function means that the growth rate remains constant over time, which would be represented as a horizontal line if you were to plot the growth rate against time.
So, your interpretation is correct: a horizontal line representing the growth rate on a plot with time on the X-axis is indicative of exponential growth.
1. Starting with any three digit number
n (such as
n = 625) we
obtain a new number
f(n) which is equal to the sum of the
three digits of
n, their three products in pairs, and the product
of all three digits.
(i) Find the value of n/f(n) when
n = 625. (The answer is
an integer!)
(ii)Find all three digit numbers such that the ratio n/f(n)=1.
2. In triangle ABC the point
X lies on BC.
(i) Suppose that 6 BAC = 90◦, that
X is the midpoint of BC,
and that 6 BAX is one third of 6 BAC. What can you say
(and prove!) about triangle ACX?
(ii)Suppose that 6 BAC = 60◦, that
X lies one third of the
way from
B to
C, and that AX bisects 6 BAC. What can
you say (and prove!) about triangle ACX?
3. The sequence of integers
u0,u1,u2,u3,... satisfies
u0 = 1 and
un+1
un−1 = kun for each
n
≥ 1,
where
k is some fixed positive integer. If
u2000 = 2000, determine all possible values of
k.
4. The points Q,R lie on the circle
γ, and
P is a point such
that PQ,PR are tangents to
γ. A is a point on the extension
of PQ, and
γ′ is the circumcircle of triangle PAR. The circle
γ′ cuts
γ again at
B, and AR cuts
γ at the point
C. Prove
that 6 PAR
= 6 ABC.
5. An increasing sequence of integers is said to be alternating
if it starts with an odd term, the second term is even, the
third term is odd, the fourth is even, and so on. The empty
sequence (with no term at all!) is considered to be alternating.
Let
A(n) denote the number of alternating sequences which
only involve integers from the set {1, 2,... ,n}. Show that
A(1) = 2 and
A(2) = 3. Find the value of
A(20), and prove
that your value is correct.
9
5
Ah, that's a shame. I was hoping you could help me with a maths problem.
If you give someone 45 billion somethings, but you don't actually have the 45 billion somethings to give them then how many days can you stay in office?
Please show your workings.
5
3
Have you grasped exponential growth yet?
2
3
did you hear about the constipated mathematician?
He worked it out with a pencil.
0
3
Post the problem here. Several posters should be able to do it fairly quickly.
Trying to help.
2
4
Saw this and thought of you riskers old chap
2
6
Hi stutter
See royalty’s post above.
0
3
Vertigo, Although it has passed into rof lore, I was quite correct on that thread as several posters at the time noted, until they were bullied into changing their minds
0
3
Not a specific problem chambers, just creating to ‘grasp’ likelihood calculations on binomial distributions. (The conceptual difference between the term of art ‘likelihood’ and what most people would consider ‘probability’. Sorted now.
0
8
Thanks royalty. I think it’s unquestionably the case that tories would be doing better than they are now if trusss had been kept
4
2
Which is obviously why you had the thread deleted so no-one could read it back. Because you were right.
0
2
https://www.rollonfriday.com/discussion/what-exponential-growth-looks
4
2
Why did you have the thread deleted risky? Don't deny it, just explain.
3
2
Iirc the X axis was and Y axis was growth rate. You missed the fact that the Y axis was growth rate and were claiming this wasn't exponential (i.e. as bad as others were claiming). The line was straight and I think slightly upward sloping so technically it wasn't exponential but super-exponential (i.e. worse!).
Is my recollection correct?
0
2
It says I can’t access it. I didn’t do anything to it. Why wouldn’t I have done it ages ago if that was the case? If you recall it’s been bumped many times.
0
2
Not quite vertigo, no
0
2
*x axis was time
1
2
Iirc, and I think I do, the label on the graph supported my conclusion
1
4
Either way I hope this ChatGPT4 response helps with your degree. Good luck.
If X axis is linear time ,Y axis is growth rate and the series shows a horizontal line, is this exponential growth
Yes, if you're plotting growth rate (specifically, the rate of change of a quantity) on the Y-axis against time on the X-axis, and the plot shows a horizontal line, this indicates that the growth rate is constant over time. In the context of functions or series, a constant growth rate typically signifies exponential growth.
To clarify, for an exponentially growing function, the formula is often given as \(f(t) = a \cdot e^{rt}\), where:
- \(a\) is the initial value,
- \(e\) is the base of the natural logarithm,
- \(r\) is the growth rate (a constant),
- \(t\) is time.
The derivative of this function, \(f'(t) = a \cdot r \cdot e^{rt}\), shows that the rate of change (growth rate) of the function is directly proportional to the function itself. The constant \(r\) in the exponential function means that the growth rate remains constant over time, which would be represented as a horizontal line if you were to plot the growth rate against time.
So, your interpretation is correct: a horizontal line representing the growth rate on a plot with time on the X-axis is indicative of exponential growth.
0
3
Productive day. Submitted my TMA
1
2
Was it on exponential growth
3
2
Youre doing a maths degree like im being admitted to all souls next week. What do you get out of being such a liar?
0
4
Marked already. 92pc. Bit lower than my other scores on this module.
2
4
.92 of a percent?
No worries sun, there’s always next time.
3
4
He spelled his name right 🤣
1
3
1
5
Book learnings never been a big thing in the plod has it Jim?
5
2
At least my teacher never called me “Dummy” on an official report.
4
3
That's a massive pwn and heh for Jim.
0
1
Congratulate me on my impressive scores.
0
1
1. Starting with any three digit number
n (such as
n = 625) we
obtain a new number
f(n) which is equal to the sum of the
three digits of
n, their three products in pairs, and the product
of all three digits.
(i) Find the value of n/f(n) when
n = 625. (The answer is
an integer!)
(ii)Find all three digit numbers such that the ratio n/f(n)=1.
2. In triangle ABC the point
X lies on BC.
(i) Suppose that 6 BAC = 90◦, that
X is the midpoint of BC,
and that 6 BAX is one third of 6 BAC. What can you say
(and prove!) about triangle ACX?
(ii)Suppose that 6 BAC = 60◦, that
X lies one third of the
way from
B to
C, and that AX bisects 6 BAC. What can
you say (and prove!) about triangle ACX?
3. The sequence of integers
u0,u1,u2,u3,... satisfies
u0 = 1 and
un+1
un−1 = kun for each
n
≥ 1,
where
k is some fixed positive integer. If
u2000 = 2000, determine all possible values of
k.
4. The points Q,R lie on the circle
γ, and
P is a point such
that PQ,PR are tangents to
γ. A is a point on the extension
of PQ, and
γ′ is the circumcircle of triangle PAR. The circle
γ′ cuts
γ again at
B, and AR cuts
γ at the point
C. Prove
that 6 PAR
= 6 ABC.
5. An increasing sequence of integers is said to be alternating
if it starts with an odd term, the second term is even, the
third term is odd, the fourth is even, and so on. The empty
sequence (with no term at all!) is considered to be alternating.
Let
A(n) denote the number of alternating sequences which
only involve integers from the set {1, 2,... ,n}. Show that
A(1) = 2 and
A(2) = 3. Find the value of
A(20), and prove
that your value is correct.
1
2
Heh@Jim
1
1
Find the first integer n > 1 such that the average of
12, 22, 32,... ,n2
is itself a perfect square.
2. How many different (i.e. pairwise non-congruent) triangles are
there with integer sides and with perimeter 1994?
3. AP, AQ, AR, AS are chords of a given circle with the property
that
6 PAQ = 6 QAR = 6 RAS.
Prove that
AR(AP + AR) = AQ(AQ + AS).
4. How many perfect squares are there (mod 2n)?
Join the discussion