What is the exponential function that best models the number of gnats the scientists have gathered after the number of hours listed in the table below?

Option A

f(x) = 12.5(1.6)^x

Step-by-step explanation:

The number of gnats the scientists have gathered

At 0 hours, they gathered 12 gnats.

Checking all the options, applying x = 0 makes the index part become 1 (Anything raised to the power zero is 1).

So, we have the following functions

f(x) = 12.5

f(x) = 12.6

f(x) = 6.2

f(x) = 1.6

This has reduced our work, as we can screen out options C and D, they are too far from 12. This leaves us with option A and B.

At 1 hour, they gathered 20 gnats.

Checking options A and B

A. f(x) = 12.5(1.6)

= 20

B. f(x) = 12.6(6.2)

By inspection, 12 × 6 is already 72,

12.6 × 6.2 will be more.

By these, we can conclude that f(x) = 12.5(1.6)^x has the best models the number of gnats the scientists have gathered after the number of hours listed in the given table.

you just switch the numbers basically so it would be 3/17