Question

the number F of bacteria in a petri dish during an experiment can be modeled by the function F(t)=5(2)^t, where t is time, in seconds, since the experiment began. find and interpret the average rate of change on the interval of [0,5]

Answer 1

$\frac{f(x+h)-f(x)}{(x+h)-x}\\\frac{f(0+5)-f(0)}{(0+5)-0}\\\frac{f(5)-f(0)}{5}\\\\f(0)=5(2)^{(0)}\\f(0)=5(1)\\f(0)=5\\f(5)=5(2)^{(5)}\\f(5)=5(32)\\f(5)=160\\\\\frac{(160)-(5)}{5}\\\frac{155}{5}\\31$

31 bacteria-per-second.