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.

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