Respuesta :
Using an exponential function, it is found that it will take 24 years for the current population of 4800 deer to reduce to 600.
What is an exponential function?
An exponential function is modeled by:
[tex]y = ab^x[/tex]
In which:
- a is the initial value.
- b is the rate of change, as a decimal.
In this problem, considering the initial value of 4800, and that the population halves every 8 years, the equation is given by:
[tex]A(t) = 4800\left(\frac{1}{2}\right)^{\frac{t}{8}}[/tex]
The population will be of 600 when A(t) = 600, hence:
[tex]A(t) = 4800\left(\frac{1}{2}\right)^{\frac{t}{8}}[/tex]
[tex]600 = 4800\left(\frac{1}{2}\right)^{\frac{t}{8}}[/tex]
[tex]\left(\frac{1}{2}\right)^{\frac{t}{8}} = \frac{600}{4800}[/tex]
[tex]\left(\frac{1}{2}\right)^{\frac{t}{8}} = \frac{1}{8}[/tex]
[tex]\left(\frac{1}{2}\right)^{\frac{t}{8}} = \left(\frac{1}{2}\right)^3[/tex]
Hence:
t/8 = 3.
t = 24.
It will take 24 years for the current population of 4800 deer to reduce to 600.
More can be learned about exponential functions at https://brainly.com/question/25537936
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