Question

oil consumption is increasing at a rate of 2.2% per year. What is the doubling time? by what factor will oil consumption increase in a decade?

Answer 1

Have you learned about the rule of 70 when figuring out doubling time?

Answer 2

no b

Answer 3

When I learned doubling time, I was taught to take the 70 and put the growth rate (r) in the denominator.
70/r(growth rate)

Answer 4

I assume that p also symbolizes growth rate, so all you have to do is write
70/2.2

Answer 5

I have 2.2%*2^10years/1 year for the second part

Answer 6

The second part of the problem?

Answer 7

by what factor will oil consumption increase in a decade

Answer 8

Well once we divide 70/2.2 we get approximately 30 years, so we can divide that in 3 to make 1 decade. Does that make sense?

Answer 9

no its doesn't I am sorry

Answer 10

I'll be honest I did not see the factor part of the equation. You may need someone else to help you with it just because i'm not quite sure i get it myself. Have a good day!

Answer 11

thanks for trying

Answer 12

ok, correct if I'm wrong

if today is 2.2%
in a year will be
2.2 + 2.2
the year after that will be
2.2 + 2.2 + 2.2
and then after that a year
2.2 + 2.2 + 2.2 + 2.2

Answer 13

so it really is
$$
\sum_{n=1}^\infty 2.2^n
$$

Answer 14

so, to know what will it be in 10 years, just make n = 10 :)

so, when will it double, that is, the increment will reach 100% to make the current 100% double or 200% of the current oil price
when \(2.2^n = 100\)

Answer 15

$$
2.2^n = 100\\
\text{using log cancellation rule}\\
log_{2.2}(2.2^n) = log_{2.2}(100)\\
n = log_{2.2}(100)\\
\text{use log change of base rule}
\implies
n = \cfrac{log(100)}{log(2.2)}
$$

Answer 16

well, not a sequence per se, just an exponential growth, with the sigma notation :)