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)

Question

Responses

f(x)=50(0.93)x
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(1.7)x
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(1.07)x
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 represent a population that grows at a rate of 7%, we use the formula for exponential growth, which is given by:

\[ f(x) = A(1 + r)^x \]

Where:

• \( A \) is the initial amount (in this case, 50 insects),
• \( r \) is the growth rate (7% as a decimal is 0.07),
• \( x \) is the time in consistent intervals (e.g., weeks, months, etc.).

Given these parameters, we can calculate the function:

1. The growth rate is 7%, so \( 1 + r = 1 + 0.07 = 1.07 \).
2. The initial population is 50.

Thus the function representing the population after \( x \) time intervals is:

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

Among the options provided, the correct one is:

f(x) = 50(1.07)^x