A pheasant farmer started her farm with 120 pheasants. An analysis of her records should that her pheasant population had increased by 15% each year. The farmer wants to determine a model of pheasant population growth using an exponential function. According to her model, what will the pheasant population be in 10 years?

Question

Mathematics

Tyrone

22 January, 13:52

A pheasant farmer started her farm with 120 pheasants. An analysis of her records should that her pheasant population had increased by 15% each year. The farmer wants to determine a model of pheasant population growth using an exponential function. According to her model, what will the pheasant population be in 10 years?

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Answers (1)

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Denzel Graham · Answer 1

Step-by-step explanation:

We would apply the formula for exponential growth which is expressed as

y = b (1 + r) ^ t

Where

y represents the population after t years.

t represents the number of years.

b represents the initial population.

r represents rate of growth.

From the information given,

b = 120

r = 15% = 15/100 = 0.15

Therefore, the model of pheasant population growth is

y = 120 (1 + 0.15) ^t

y = 120 (1.15) ^t

When t = 10 years,

y = 120 (1.15) ^10

y = 485

The population would be 485 pheasants