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ginny is studying a population of frogs. she determines that the population is decreasing at an average rate of 3% per year. when she began her study, the frog population was estimated at 1,200. which function represents the frog population after x years? f(x) = 1,200(1.03)x f(x) = 1,200(0.03)x f(x) = 1,200(0.97)x f(x) = 1,200(0.97)x

Verified Answer :

olemakpadu

if they are decreasing at 3% , net = 100% - 3% = 97%

Reduction rate = 97% = 0.97

After 1st year =  12000.97

After 2nd year = 1200(0.97)(0.97) = 1200(0.97)²

After 3rd year =   1200(0.97)(0.97)(0.97) = 1200(0.97)³

After x years, =   1200(0.97)ˣ

Therefore, function  f(x) = 1200(0.97)ˣ 

The population decreasing rate for x year can be calculated by determine the yearly population decreasing.

The population rate after \(x\) year is \(f(x)=1200(0.97)^x\).

Given:

The average decreasing rate is \(3\%\).

The frog population is \(1200\).

Calculate the reduction rate.

\(\rm Net=100\%-3\%\\Net=97\%\)

Calculate the decrease rate after 1 year.

\(f(1)= 1200\times 0.97\)

Calculate the decrease rate after 2 year.

\(f(2)=1200\times (0.97)\times (0.97) \\f(2)= 1200\times (0.97)^2\)

Calculate the decrease rate after 3 year.

\(f(3)=1200\times (0.97)\times(0.97)\times(0.97) \\f(3)= 1200\times(0.97)^3\)

Calculate the decrease rate after \(x\) year.

\(f(x)=1200\times (0.97)^x\)

Thus, the correct option is \(f(x)=1200\times (0.97)^x\).

Learn more about decreasing rate here:

https://brainly.in/question/34468945

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