Estimate to the nearest integer the doubling time of the fun

Estimate to the nearest integer the doubling time of the function f(t) shown below. Use your estimate and the vertical intercept to write an equation for f(t).

So the doubling from 3 to 6 is 7. How do I get to a fuction?

Solution

We have ( 7, 6) and (14, 12)

as we can see that 7 is the doubling time ( 6 ----> 12)

y intercept = 3

So, f(t) = fo(2)^t/T

T = 7 ; fo = 3

f(t) = 3(2)^(t/7)