Question

The function below describes the population of caribou in a tundra, where f(t) represents the number of caribou, in hundreds, and t represents the time, in years.

f(t)=1.8(1.2)^t


Initially, the tundra has _____ caribou, and every ____ , the number of caribou increases by a factor of ____ .

Answer 1

180

1 year

1.2

Explanation:

got it correct on edmentum

Answer 2

Initially, the tundra has 180 caribou, and every year , the number of caribou increases by a factor of 1.2 .

Explanation:

"Initially" generally means "when t=0." Put 0 where t is in the function and evaluate it:

f(0) = 1.8(1.2)^0 = 1.8(1) = 1.8 . . . . . hundreds

1.8 hundreds is 1.8×100 = 180.

__

t is in years, so the simplest choice for the second blank in the statement is "year".

__

The exponent of 1.2 is t, which means that 1.2 is a factor of the expression the number of times specified by t.

for t=0, f(0) = 1.8

for t=1, f(1) = 1.8(1.2)

for t=2, f(2) = 1.8(1.2)(1.2)

for t=3, f(3) = 1.8(1.2)(1.2)(1.2)

Perhaps you can see that every year, the number increases by a factor of 1.2.

_____

You could put "3 years" in the second blank, then the third blank would be 1.2³ = 1.728. While correct, it is probably not what is expected by your answer checker.