How to solve these math problems pertaining to logarithms and exponents? 1 . A population doubles in size every 15 years. Assuming exponential growth, find the a. annual growth rate. please show me...

How to solve these math problems pertaining to logarithms and exponents?

1 . A population doubles in size every 15 years. Assuming exponential growth, find the a. annual growth rate. please show me step by step instructions on how you solves each problem! thanks you very much !

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lfryerda eNotes educator | Certified Educator

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If you have more than one question, you need to make separate posts.

To determine the annual growth rate, you need to determine how much the population increases in a single year.

The exponential growth formula is

`A=A_0 b^t`  where A is the final amount, `A_0` is the initial amount, b=1+r is the base, r is the growth rate and t is the time in years.  In this case, we are told that after 15 years, we have the population doubled, which means that when t=15, `A=2A_0` .  Then:

`2A_0=A_0 b^15`  divide by `A_0`

`2=b^15`  take 15th root

`2^{1/15}=b`   but b=1+r

`2^{1/15}=1+r`   solve for r

`r=2^{1/15}-1`

`r approx 0.0473`

The annual growth rate is approximately 4.73%.

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