• anonymous
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)
  • Stacey Warren - Expert
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  • schrodinger
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  • dumbcow
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
  • anonymous
I got the same answer on my test, thanks for clarifying!

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