Question

The initial size of a bacteria culture is 800. After 4h there are 7200 bacteria. Using Ce^kt, the simplified equation is y = 800(9)^t/4 Find the rate of growth after 6h. (I am sure that you have to find the derivative and sub 6 for t, I just don't know how)

Answer 1

you are correct to find the rate at t=6 you need differentiate the function and evaluate at t=6.
to find the derivative you need to know the chain rule and the derivative of the form a^x
d/dx a^x = ln(a)*a^x
chain rule says take derivative of outer function times derivative of inner function.
outer = 800*9^u where u = x/4 this is the inner function
derivative of outer is 800*ln(9)*9^u
derivative of inner is 1/4
put them together => (1/4)*800*ln(9)*9^(x/4)
Now plug in x=6
=>(1/4)*800*ln(9)*9^(6/4)
=> i get an answer of 11865.01
Hope this helps

Answer 2

I got the same answer on my test, thanks for clarifying!