Example in book: Energy consumption for some city is 7000 megawatts (MW) and increases at the rate of 2% per year.

a. Find the function which gives power consumption

The book gives

$\displaystyle P(1)=1.02$

$\displaystyle P_0 = 1.02(7000)=7140$

$\displaystyle P(1)=P_0e^{kt}$

$\displaystyle 7140=7000e^{k}$

$\displaystyle k=.0198$

$\displaystyle P(t)=7000e^{.0198t}$

Which means the growth rate is .0198 or 1.98%. But the growth rate (and I copied pretty much the exact question wording) is 2%. The question says it grows 2%every year. That means the growth rate is 2%! End of story.

Butkis the growth rate. The equation iseraised to the growth rate timest. Shouldn't the answer be

$\displaystyle P(t)=7000e^{.02t}$

What gives?

Thanks.