Posted by **Megan** on Sunday, October 14, 2012 at 9:29pm.

In 1960, the population was 291000. In 1970, the population was 480000. Assuming exponential growth, what is the annual percent rate? and doubling time?

The answers are 5.13% and 14 years. I do not know how to get this though :( Please help!

- Math. Increases -
**Megan**, Sunday, October 14, 2012 at 9:39pm
Please help! test tomorrow

- please help. Test tomorrow -
**Megan**, Sunday, October 14, 2012 at 9:40pm
thanks:)

- Math. Increases -
**Reiny**, Sunday, October 14, 2012 at 9:45pm
Let's use the equation

number = a e^kt, where a is the initial value, k is the rate of growth and t is the number of years

so let 1960 correspond to a time of t = 0

then 1970 ----> t = 10

also a = 291000

480000 = 291000 e^10k

1.64948 = e^10k

take ln of both sides

ln 1.64948 = ln e^10k = 10k

k = .50046/10 = .050046 = 5.005 %

(no idea how they got their answer, it is not correct)

check:

291000 e^(10(.050046)) = 479999

pretty close to 480000

their answer:

291000 e^(10(.0513)) = 486056 , too big

for doubling time:

2 = 1(e^.050046t)

ln 2 = .050046t

t = ln 2/.050046 = 13.8 years.

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