Question

A bird sanctuary used to receive 10,000 birds per year. The number of birds migrating to the sanctuary is decreasing at the rate of 5% each year. Identify the exponential decay function that models the situation. Then find the bird population after 4 years.

a- y = 10000(0.5); 7800
b- y = 10000(0.95)t ; 8000
c- y = 10000(0.9)t ; 7900
d- y = 10000(0.95)t ; 8145

Answer 1

d. y = 10000(0.95)^t ; 8145

Explanation:

The population decay can be modeled by the exponential function ...

y = a·b^t

where 'a' is the initial population, and 'b' is the decay factor. The decay factor is 1 more than the decay rate:

b = 1 +(-5%) = 0.95

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For an initial population of a=10,000, the exponential function is ...

y = 10000·0.95^t

When t=4, the population is modeled to be ...

y = 10000·0.95^4 = 10000(0.81450625) ≈ 8145

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The function is ...

y = 10000·(0.95)^t

y = 8145 . . . . . after 4 years