Question

The population of a current species of rhinoceros is declining at a rate of 6% each year. There are currently only 82 rhinoceroses remaining. Create an exponential function to model the population decline. Which of the following options correctly models the decline?(1 point) Responses f(x)=82(0.94)x f of x is equal to 82 times 0 point 9 4 to the x th power f(x)=82(1.06)x f of x is equal to 82 times 1 point 0 6 to the x th power f(x)=82(0.06)x f of x is equal to 82 times 0 point 0 6 to the x th power f(x)=82(1.6)x

Answer 1

To model the population decline of the rhinoceros, we can use an exponential decay function of the form:

\[ f(x) = P_0 \cdot (1 - r)^x \]

where:

• \( P_0 \) is the initial population,
• \( r \) is the rate of decline (as a decimal),
• \( x \) is the number of years.

Given:

• The initial population \( P_0 = 82 \),
• The rate of decline \( r = 6% = 0.06 \).

Thus, \( 1 - r = 1 - 0.06 = 0.94 \).

So the exponential decay function modeling the population decline is:

\[ f(x) = 82 \cdot (0.94)^x \]

Therefore, the correct option that models the decline is:

f(x) = 82(0.94)^x.