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Algebra 2 Help Logarithms and Exponential Growth factors:?
4.The current exponential function P(x) measures the fish population’s growth monthly. Using complete sentences explain how to find the rate of growth every week.
5.The National Fish and Wildlife Foundation has asked you to calculate when the population of the fish reaches 500. Show all of your work.
6.The computer system you need to input the function into only works in logarithms of base 10. Using complete sentences, explain how to convert your exponential function P(x) in a logarithmic one and then into a base 10 logarithm.
P(x) = (20 * 5) ^ x
1 Answer
- Jeff AaronLv 75 years ago
4.
P(x) = (20 * 5)^x
P(x) = 100^x
So presumably after x months, the fish population is 100^x
The average number of weeks in a month is 4.348125
So after w weeks, that's about w/4.348125 months, so the fish population would be:
100^(w/4.348125)
That's about 2.8838215121879491393624174945154^w
5.
100^x = 500
Since x is a real number:
x = log[100](500)
x =~ 1.3494850021680094023931305526378
6.
P(x) = 100^x
P(x) = (10^2)^x
P(x) = 10^(2x)
