Westonci.ca is the ultimate Q&A platform, offering detailed and reliable answers from a knowledgeable community. Get accurate and detailed answers to your questions from a dedicated community of experts on our Q&A platform. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.
Sagot :
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
#SPJ1
Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.
