Problema Solution

Find the formula of an exponential function passing through the points (3,71) and (9,93) for continuous growth.

Answer provided by our tutors

For this question, we will use the general exponential growth equation: y=ae^(kt). From the given information we can write:


71=ae^(k3)

93=ae^(k9)


This gives us two equation with two unknowns (a, k). Rearranging, we get:


ln(71)-ln(a)=3k

ln(93)-ln(a)=9k


Subtracting the second equation from the first, we get:


ln(71)-ln(93)=-6k


Solving for 'k', we get:


k=0.01796


We can use this to plug into one of the earlier equation to find 'a':


71=ae^(0.01796*3)


Solving for a, we get:


a=67.28


Therefore, the general equation is:


y=67.28 e^(0.01796 t)