Question

currently, there are 1,460 wolves in scataway national park. if the population of wolves is growing at a rate of 6% every year, which function represents the number of wolves in scataway national park in t years?
a. $w(t) = 1,460(0.94)^t$
b. $w(t) = 1,460(0.06)^t$
c. $w(t) = 1,460(1.06)^t$
d. $w(t) = (1,460)(1.06)t$

Explanation:

Step1: Recall exponential growth formula

The standard exponential growth function is $W(t) = W_0(1+r)^t$, where $W_0$ is the initial population, $r$ is the growth rate, and $t$ is time in years.

Step2: Identify given values

Initial population $W_0 = 1460$, growth rate $r = 0.06$ (6% converted to decimal).

Step3: Substitute values into formula

Substitute $W_0$ and $r$ into the formula: $W(t) = 1460(1+0.06)^t = 1460(1.06)^t$

Step4: Match with options

Compare the derived function to the provided options.

Answer:

C. $W(t) = 1,460(1.06)^t$