Question

3. A sample of single celled algae from Chequamegon Bay provided an estimate of 100,000 cells on the initial sampling date. Ten days later, the population size was estimated to be 500,000 cells. Calculate the intrinsic growth rate (r) for the population. Use the exponential model of population growth to predict the size of the population after another 10 days.

Answer 1

Number of population at initial sampling date is 100,000

After 10 days, the population size is 500,000

dN/dt = rN

rN = (500,000 - 100,000)/ 10

rN = 40,000

r = 40,000/ 500,000

= 0.08

= 8%

The size of the population after 10 days,

x(t) = x₀ × (1 + r) ^t

= 500,000 x (1 + 0.08)^10

= 1079462