A scientist is growing bacteria in her lab. She finds that the number of bacteri

Question

A scientist is growing bacteria in her lab. She finds that the number of bacteria per microliter in her sample can be described by the following function:

f ( t ) = 200 + 125 t 2

Here, t is measured in hours after the start of the experiment.

What is the average growth rate of her sample between hours 5 and 15 of her experiment?

Average growth rate :

What is the growth rate of her sample at hour 15 of her experiment?

Growth rate :

At what rate is the growth rate changing at this time?

Rate of change of growth rate :

Explanation / Answer

a) average growth rate can be calculated by the formula-[f(b)-f(a)]/(b-a)

f ( t ) = 200 + 125 t2

for interval (5,15)

average growth rate=[f(15)-f(5)]/(15-5)=(28325-3325)/10 =2500 answer

b) at hour 15 instantaneous growth change is

df/dt=250t , at t=15

df/dt =3750 answer

c) rate of change of growth rate = f''(t)= d2f/dt2 = 250 answer

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