1. Which function represents an initial population that increases 22% per year where A represents the initial value and X represents time in years?
A. Y=A(0.22)^x
B. Y=A(0.68)^x
C. Y=A(1.22)^x
D. Y=A(1.68)^x
I do not get how to solve this problem. Any help would be great. Thank you!
at the end of the first year, one has the original amount + 22percent of the original, or a factor of 1.22.
Answer C
Oh ok, I understand that. Thank you so much!
To find the function that represents an initial population that increases 22% per year, we can break down the information given.
Given:
- A represents the initial value
- X represents time in years
- The population increases 22% per year
To represent the increase, we need to multiply the initial value by a factor. This factor is found by adding 100% (the initial value) to the 22% increase.
The factor representing the increase is 100% + 22% = 122%.
Therefore, the function that represents an initial population that increases 22% per year is:
Y = A * (1.22)^X
Hence, the correct answer is C. Y = A(1.22)^X.
To solve this problem, we need to identify the function that represents an initial population that increases by 22% per year. Let's analyze the options one by one:
A. Y = A(0.22)^x
This function represents an exponential decay because (0.22)^x always produces a value less than 1. Therefore, it does not represent an increasing population over time.
B. Y = A(0.68)^x
Similar to option A, this function represents an exponential decay because (0.68)^x always produces a value less than 1. It does not represent an increasing population.
C. Y = A(1.22)^x
This function represents an initial population that increases by 22% per year. Every time x increases by 1 (representing one year), (1.22)^x will give us a factor of 1.22, which corresponds to a 22% increase. Therefore, this option is a plausible representation of an increasing population.
D. Y = A(1.68)^x
This function represents an initial population that increases by 68% per year. Every time x increases by 1 (representing one year), (1.68)^x will give us a factor of 1.68, which corresponds to a 68% increase. This option represents a population growth greater than the given 22%.
To summarize, option C, Y = A(1.22)^x, represents an initial population that increases by 22% per year. Therefore, the correct answer is C.