Question

the function $f(x) = 10(1.05)^x$ models the population of a species after $x$ years. does this function represent exponential growth or decay? show your work here

Explanation:

Step1: Recall exponential form

The general form of an exponential function is \( f(x) = a(b)^x \), where \( a \) is the initial amount and \( b \) is the base.

Step2: Analyze the base

For the function \( f(x) = 10(1.05)^x \), the base \( b = 1.05 \).

• If \( b > 1 \), the function represents exponential growth.
• If \( 0 < b < 1 \), the function represents exponential decay.

Since \( 1.05 > 1 \), the function shows exponential growth.

Answer:

Exponential Growth