Exponential Functions (PLEASE HELP ME CONFIRM

Question

The exponential function y(x) = Ce^αx satisfies the conditions y(0) = 0 and y(1) = 7

A. Find the constants C and α

C= 9

α = -0.251

B. find y(2)

Since I got the answers above, would y(2) therefore be 5.448 if I round 3 decimal places?

Answer 1

It seems like the initial condition was mistyped and it should be y(0)=9, which makes C=9 correct and α = ln(7/9).

Now we can solve for y(2):

y(2)=9*e^[2*ln(7/9)]=9*(7/9)^2= 49/9 or 5.444 repeating.