Question

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−0.5t where t is measured in hours. at time t = 0 the population is 20 cells and is increasing at a rate of 8 cells/hour. find the values of a and
b.

Answer 1

Answer:

a=40.33 and b = -0,5041

Step-by-step explanation:

given that

n = a[1 + b^(e - 0.5t)]

When t =0 we have 20 = a(1+b)  ... i

Increase rate = 8 cells per hour

Hence when t=1, n =28

i.e. 28 = a(1+be^(-0.5)) = a(1+0.6066b) = 28 ... i

Divide ii by i

28/20 = 1+0.6066b/1+b

28+28b = 20+12.1312b

15.869b= -8

b = -0.5041

Substitute in 20 = a(1+b)

20 = a(0.4959)

a=40.33

thus answer is a = 40.33 and b=-0.5041