Question

4) The number of fish, N, in a pond is decreasing according to the model No= ab' + 40,10 where a and b are positive constants, and t is the time in months since the number of fish in the pond was first counted. At the beginning 840 fish were counted. a. Find the value of a. b. After 4 months 90 fish were counted. Find the value of b. c. The number of fish in the pond will not decrease below p. Write down the value of p. Answers/Work: b C:

Answer 1

N (t) = ab^-t +40, t ≥ 0

when t=0, N (t) = 840

a)

840 = ab^0 +40

840 = a (1) +40

840 = a +40

840-40 = a

a= 800

b)

t=4, N(4)=90

90 = 800 b^(-4) +40

90 -40= 800 b^(-4)

50 = 800 b^(-4)

50/800 = b^(-4)

0.0625 = b^(-4)

0.0625 = 1/ b^4

b^4 = 1/0.0625

b= 4√ 16

b= 2

c) p=40