Question

what does the value 5,200 represent in the function? a growth factor b number of years c growth rate d initial population what does the value 1.1 represent in the function? a growth factor b number of years c growth rate d initial population

Explanation:

First Question (About 5,200):

In a typical exponential growth function (e.g., \( P(t)=P_0(1 + r)^t \), where \( P_0 \) is initial population, \( r \) is growth rate, \( (1 + r) \) is growth factor, and \( t \) is time), the initial value (like 5,200 here) represents the starting quantity, which is the initial population. A growth factor is a multiplier (e.g., 1.1), the number of years is a variable (like \( t \)), and growth rate is a percentage - related value (e.g., 0.1 for 10% growth). So 5,200 is the initial population.

In the exponential growth model \( P(t)=P_0(1 + r)^t \), the term \( (1 + r) \) is the growth factor. Here, 1.1 would be \( 1 + r \) (if \( r = 0.1 \) or 10% growth rate). The initial population is the starting value (like 5,200), the number of years is a variable, and growth rate is \( r \) (not the 1.1 itself). So 1.1 is the growth factor.

Answer:

D. initial population

Second Question (About 1.1):