A population of 59 foxes in a wildlife preserve quadruplets in size every year. The function, y=59•4x where x is the number of years models of the population growth. Using the given function how many foxes will there be after 5 years?
To find the number of foxes after 5 years, we substitute x = 5 into the function:
y = 59 * 4^5
y = 59 * 1024
y = 60976
Therefore, there will be 60,976 foxes after 5 years.
A student was trying to write an exponential function to represent a fish population in a local stream decreasing at a rate of 4% per year. The original population was 48,000. The student made an error when writing their exponential function find and explain the error in the students work below
y=48,000(1.04)^x
The error in the student's work lies in the exponent of the exponential function. They mistakenly wrote (1.04)^x, indicating an increase of 4% per year, instead of a decrease of 4% per year.
To represent a decrease of 4% per year, the correct exponential function should be:
y = 48,000(0.96)^x
In this case, the base of the exponent is 0.96, indicating that the population will decrease by 4% each year.
To find out how many foxes there will be after 5 years using the given function y = 59•4^x, we need to substitute x with 5:
y = 59 • 4^5
First, we calculate 4^5:
4^5 = 4 • 4 • 4 • 4 • 4 = 1024
Now we can substitute this value into the equation:
y = 59 • 1024
Solving the equation:
y = 59 * 1024 = 60416
Therefore, after 5 years, there will be a population of 60,416 foxes in the wildlife preserve.