Question

What is the exponential function that best models the number of gnats the scientists have

Answer 1

Answer:

  (b)  f(x) = 12.5(1.6^x)

Step-by-step explanation:

An exponential model is generally of the form ...

  f(x) = a·b^x

where 'a' is the initial value (for x=0), and 'b' is the growth factor, the multiplier when x increases by 1.

Growth factor

The ratio of the f(x) values for x=0 and x=1 is 20/12 ≈ 1.67. A number close to this will be the growth factor in the exponential function. There is only one answer choice showing a growth factor near 1.6. (Eliminates choices A, C, D.)

An exponential regression model can be produced by many graphing calculators and spreadsheets. The attachment shows a model that has the values matching choice B.