Question

Use the table provided to find an exponential model ƒ(x) = abx, where ƒ is the population of Florida, and the input is the number of years since 2004. Approximate to the thousandth’s place.

ƒ(x) = 17,385,430 • (1.023)x

ƒ(x) = 17,789,864 • (1.023)x

ƒ(x) = 17,385,430 • (0.977)x

ƒ(x) = 17,385,430 • (0.023)x

Answer 1

Answer:
`F(x) = 17,385,430 (1.023)^x`

Explanation:

Here, The function that describes the population of Florida after x years,

`F(x) = ab^x` -------- (1)

Where a is the initial population of Florida and b is the growth factor.

Since, according to the table a = 17,385,430 and f(x) = 17,789,864

When x= 1

Thus, from equation (1),

`17,789,864 = 17,385,430( b)^1`

⇒ b = 17,789,864/ 17,385,43= 1.0232628126≈ 1.023

By Putting the values of a and b in equation (1),

Required function is,
`F(x) = 17,385,430 (1.023)^x`