Question

A population of 12,000 fish has a growth rate of 4% each year. Write a model for the situation. How many years will it take of the population to reach 20,000

Answer 1

13years

Explanation:

Using the formula for calculating the compound interest expressed as;

A =P(1+r)^n

P = 12000

rate r = 4% = 0.04

Amount after 4 years A = 20,000

Substitute into the formula and solve for p

20,000 = 12,000(1+0.04)^t

20,000/12000 = (1.04)^t

1.67 = (1.04)^t

Take the ln of both side

ln1.67 = ln(1.04)^t

ln1.67 = t ln 1.04

t = ln1.67/ln1.04

t = 0.5108/0.0392

t = 13.03

hence it will take approximately 13years to reach 20,000