Westonci.ca connects you with experts who provide insightful answers to your questions. Join us today and start learning! Get quick and reliable solutions to your questions from a community of experienced experts on our platform. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.
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
Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.
