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Part $1$

When observations begin at

tequals$=0,$

a cell culture has

$16001600$

cells and continues to grow according to the function

p left parenthesis t right parenthesis equals $1600$ e Superscript tp$($t$)=1600$et$,$

where p is the number of cells and t is measured in days.

a$.$ Compute

p prime left parenthesis t right parenthesisp$($t$).$

What units are associated with the derivative and what does it$$ measure?

b$.$ On the interval

$[0,55]$

when is the growth rate

p prime left parenthesis t right parenthesisp$($t$)$

the$$ least? When is it the$$ greatest?

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Part $1$

a$.$

p prime left parenthesis t right parenthesisp$($t$)$equals$=$enter your response here

$($Type an exact answer in terms of

ee$.)$