Exponential Functions in Context Quick Check

Question

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Question
Create an exponential function to represent a population of 50 insects that is growing at a rate of 7%. Which of the following functions is accurate?(1 point)
Responses

f(x)=50(1.7)x
f left parenthesis x right parenthesis equals 50 left parenthesis 1.7 right parenthesis superscript x baseline

f(x)=50(0.93)x
f left parenthesis x right parenthesis equals 50 left parenthesis 0.93 right parenthesis superscript x baseline

f(x)=50(1.07)x
f left parenthesis x right parenthesis equals 50 left parenthesis 1.07 right parenthesis superscript x baseline

f(x)=50(0.07)x

Answer 1

To model the exponential growth of a population of insects that starts at 50 and grows at a rate of 7%, the correct exponential function to represent this situation is:

\[ f(x) = 50(1.07)^x \]

Here’s why:

• The initial population is 50, which is the starting value.
• A growth rate of 7% translates to a growth factor of \( 1 + 0.07 = 1.07 \).
• The variable \( x \) typically represents time in units of your choice (e.g., days, months, years).

Thus, the accurate function is:

f(x) = 50(1.07)^x