Question

In a certain flock of pigeons, the population is declining at a rate of 5% per year.

If there are currently 140 pigeons in the flock, create an exponential decay function to model the problem. Let y
represent the number of pigeons after x
years. Explain why you chose your answer using one of the answering options provided.

(1 point)
Responses

y=140(0.5)x

y is equal to 140 times 0 point 5 to the x th power

y=140(0.95)x

y is equal to 140 times 0 point 9 5 to the x th power

y=140(0.05)x

y is equal to 140 times 0 point 0 5 to the x th power

y=140(1.05)x

y is equal to 140 times 1 point 0 5 to the x th power
Question 2
Explain why (by speaking) you chose your answer above? (1 point)
Question 3
Explain (by typing) why you chose your answer above.(1 point)

Answer 1

Correct choice: y = 140(0.95)^x

Spoken explanation (short): A 5% decline means each year you keep 95% of the pigeons, so multiply by 0.95 each year.

Typed explanation: The general exponential model is y = initial × (growth factor)^x. A 5% decrease means the yearly factor = 1 − 0.05 = 0.95, and the initial population is 140, so y = 140(0.95)^x. (y = 140(0.5)^x would be a 50% yearly decrease, 140(0.05)^x would leave only 5% each year, and 140(1.05)^x would be 5% growth, not decay.)