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There are 50 deer in a particular forest. The population is increasing at a rate of 15% per year. Which exponential growth function represents
the number of deer y in that forest after x months? Round to the nearest thousandth.
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Answer:
The expression that represents the number of deer in the forest is
y(x) = 50*(1.013)^x
Step-by-step explanation:
Assuming that the number of deer is "y" and the number of months is "x", then after the first month the number of deer is:
y(1) = 50*(1+ 0.15/12) = 50*(1.0125) = 50.625
y(2) = y(1)*(1.0125) = y(0)*(1.0125)² =51.258
y(3) = y(2)*(1.0125) = y(0)*(1.0125)³ = 51.898
This keeps going as the time goes on, so we can model this growth with the equation:
y(x) = 50*(1 - 0.15/12)^(x)
y(x) = 50*(1.013)^x
The exponential growth function that represents the number y of deer in that forest after x months is 50 × [tex](1.013)^{x}[/tex].
An exponential function is a nonlinear function that has the form of
y=[tex]ab^{x}[/tex],wherea≠0,b>0. An exponential function with a > 0 and b > 1, like the one above, represents an exponential growth and the graph of an exponential growth function rises from left to right.
There are 50 deer in a particular forest.
The population is increasing at a rate of 15% per year.
Assuming that the number of deer is 'y' and the number of month is 'x' then after the first month the number of deer is
y(x) = 50 × [tex]1+(\frac{0.15}{12} )[/tex]
= 50 × 1.0125
= 50.625
y(2) = y(1) × (1.0125)
= y(0) × [tex](1.0125)^{2}[/tex]
= 51.258
y(3) = y(2) × (1.0125)
= y(0) × [tex](1.0125)^{2}[/tex]
= 51.898
y(x) = 50 × [tex](1-\frac{0.15}{12} )^{x}[/tex]
= 50 × [tex](1.013)^{x}[/tex]
Hence, the exponential growth function that represents the number y of deer in that forest after x months is 50 × [tex](1.013)^{x}[/tex].
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