j0eanniesalov2eever
contestada

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

Respuesta :

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

Reduction rate = 97% = 0.97

After 1st year =  1200*0.97

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 [tex]x[/tex] year is [tex]f(x)=1200(0.97)^x[/tex].

Given:

The average decreasing rate is [tex]3\%[/tex].

The frog population is [tex]1200[/tex].

Calculate the reduction rate.

[tex]\rm Net=100\%-3\%\\Net=97\%[/tex]

Calculate the decrease rate after 1 year.

[tex]f(1)= 1200\times 0.97[/tex]

Calculate the decrease rate after 2 year.

[tex]f(2)=1200\times (0.97)\times (0.97) \\f(2)= 1200\times (0.97)^2[/tex]

Calculate the decrease rate after 3 year.

[tex]f(3)=1200\times (0.97)\times(0.97)\times(0.97) \\f(3)= 1200\times(0.97)^3[/tex]

Calculate the decrease rate after [tex]x[/tex] year.

[tex]f(x)=1200\times (0.97)^x[/tex]

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

Learn more about decreasing rate here:

https://brainly.in/question/34468945

Otras preguntas