Question

the function $f(t) = 340(1.021)^t$ can be used to estimate the population of rabbits in an urban neighborhood after $t$ years. which of the following statements are true? select two correct answers. the initial population of rabbits decreased at a rate of 2.1% the growth factor of the population of rabbits in the neighborhood is 1.021. the initial population of rabbits increased at a rate of 2.1% the initial population of rabbits in the neighborhood is 1021 rabbits. the population of rabbits after the first year is 340.

Explanation:

Step1: Identify exponential growth form

The function is $f(t) = a(b)^t$, where $a$=initial population, $b$=growth factor.

Step2: Analyze initial population

Initial population is $a=340$ (when $t=0$: $f(0)=340(1.021)^0=340$).

Step3: Analyze growth factor

Growth factor is $b=1.021$ (base of the exponent).

Step4: Analyze growth rate

Growth rate = $b-1=0.021=2.1\%$ (increase, not decrease).

Step5: Check first year population

First year population: $f(1)=340(1.021)≠340$.

Answer:

B. The growth factor of the population of rabbits in the neighborhood is 1.021.
C. The initial population of rabbits increased at a rate of 2.1%