An initial population of 175 quail increases at an annual rate of 22%. Write an exponential function to model the quail population. What will the approximate population be after 5 years? (1 point) Responses ƒ(x) = 175(0.22)x; 473 ƒ( x ) = 175(0.22) x ; 473 ƒ(x) = (175 • 0.22)x; 84,587,005 ƒ( x ) = (175 • 0.22) x ; 84,587,005 ƒ(x) = 175(22)x; 901,885,600 ƒ( x ) = 175(22) x ; 901,885,600 ƒ(x) = 175(1.22)x; 473

Question

An initial population of 175 quail increases at an annual rate of 22%. Write an exponential function to model the quail population. What will the approximate population be after 5 years? (1 point) Responses ƒ(x) = 175(0.22)x; 473 ƒ( x ) = 175(0.22) x ; 473 ƒ(x) = (175 • 0.22)x; 84,587,005 ƒ( x ) = (175 • 0.22) x ; 84,587,005 ƒ(x) = 175(22)x; 901,885,600 ƒ( x ) = 175(22) x ; 901,885,600 ƒ(x) = 175(1.22)x; 473

Answer 1

The correct exponential function to model the quail population is ƒ(x) = 175(1.22)^x.

To find the approximate population after 5 years, we can substitute x = 5 into the exponential function:

ƒ(5) = 175(1.22)^5 ≈ 473.263

So, the approximate population after 5 years will be 473.