The number of yeast cells in a laboratory culture increases rapidly initially but levels off eventually. The population is modeled by the function n = f(t) = a 1 + be−0.7t where t is measured in hours. At time t = 0 the population is 30 cells and is increasing at a rate of 18 cells/hour. Find the values of a and b.

a = 30

b = 6/7

Step-by-step explanation:

The number of yeast cells after t hours is modeled by the following equation:

In which a is the initial number of cells.

At time t = 0 the population is 30 cells

This means that

So

And increasing at a rate of 18 cells/hour.

This means that f'(0) = 18.

We use this to find b.

So

Then, it's derivative is:

We have that:

f'(0) = 18

So

Then

step-by-step explanation:

their are no angles. sorry cant .

50

step-by-step explanation: