Question

biologists are tracking the growth of a rabbit population. there were 45 rabbits initially and the population is quadrupling every year. which of the following equations can be used to find when the population of rabbits will be equal to 720? a. $720 = 45(4)^{x}$ b. $720 = 45 + 4^{x}$ c. $720 = (180)^{x}$ d. $720 = 4(45)^{x}$

Explanation:

Step1: Recall exponential growth formula

The general formula for exponential growth is \( P = P_0 \cdot r^t \), where \( P \) is the final amount, \( P_0 \) is the initial amount, \( r \) is the growth rate, and \( t \) is time.

Step2: Identify values from problem

Here, initial population \( P_0 = 45 \), growth rate \( r = 4 \) (since it's quadrupling), final population \( P = 720 \), and time is \( x \) (let's say).

Step3: Substitute into formula

Substituting into \( P = P_0 \cdot r^t \), we get \( 720 = 45(4)^x \).

Answer:

A. \( 720 = 45(4)^x \)