Question

select the correct answer from each drop - down menu.
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 $square$ caribou, and every $square$, the number of caribou increases by a factor of $square$.

Explanation:

Step1: Find initial population

For the exponential function \( f(t)=a(b)^t \), the initial value (when \( t = 0 \)) is \( a \). Here, \( a = 1.8 \), and since \( f(t) \) is in hundreds, initial number of caribou is \( 1.8\times100=180 \).

Step2: Determine time period and growth factor

The base \( b = 1.2 \) in \( f(t)=1.8(1.2)^t \) (where \( t \) is in years) means every 1 year, the population is multiplied by \( 1.2 \), so the growth factor is \( 1.2 \).

Answer:

Initially, the tundra has \(\boldsymbol{180}\) caribou, and every \(\boldsymbol{year}\), the number of caribou increases by a factor of \(\boldsymbol{1.2}\).