I need help with a calculus problem please help me?

Question

I need to figure out an exponential growth problem.. help me please?
I am not sure how to do this calculus problem... I need to know before my final.. help me smart people

The price of candy in 1962 was $.05 at an exponential growth ie. dP/dt = ce^kt and the growth rate is 9.7% to the nearest hundreth

1. Write the cost C as a function of time t years after 1962 C(t)
2 Predict cost in 2008 and 2015

Answer 1

The key in this problem is to understand what they mean by a growth rate of 9.7 %.

% means you have to divide by P
So I guess (dP/dt) / P = 0.097
or dP/dt = 0.097 P = 0.097*C/k*e^kt

But dP/dt = C*e^kt

So k = 0.097
C/k = 0.05

P = C/k * e^kt
In 2008, t = 46 years,
P = 0.05 * e^(0.097*46) = $4.33

In 2015, P = $8.54

Answer 2

The cost is .05 * e^(.097(t-1962)).

For the rest, get out your calculator. :)