Question

The population of an endangered species of insect is 480,000. The population decreases at the rate of 10% per year. Identify the exponential decay function to model the situation. Then find the population of the species after 3 years.

A: y = 480,000(1.01)t; 280,000

B: y = 480,000(1.1)t; 638,880

C: y = 480,000(0.9)t; 339,940

D: y = 480,000(0.9)t; 349,920 5
Cesium-137 has a half-life of 30 years. Identify the amount of cesium-137 left from a 150 milligram sample after 120 years.
A: 0.9375 mg
B: 9.3750 mg
C: 1.097 mg
D: 1.325 mg 6

Answer 1

D: y = 480,000(0.9)t; 349,920

Explanation:

The question requires us to model a compounding exponential decay function at a given rate for a particular period :

Using the model :

F = Fo( 1 - r)^t

Where;

F = final amount; Fo = Initial amount; r= annual rate ; t = period

Initial amount = 480,000

Rate = 10%

t = 3years

F = 480,000(1 - 0.1)^3

F = 480,000(0.9)^3

F = 480,000 × 0.729

F = 349, 920

A = (Ao / 2^(t/t1/2)

A = final amount

Ao = Initial amount

t = time or period ; t1/2 = half-life = 30 years

A = (150 / 2^(120/30))

A = (150 / 2^(4))

A = 150/16

A = 9.375mg