Hello again! You might see me a lot today. Just a heads up.
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
This is also another question that I do not get. Any help? Thank you!
My little Chode
I just guessed
Hello again! No problem, I'm here to help. Let's break down the question to find the correct answer.
The function represents an initial population that increases 22% per year. So, we're looking for a function that includes an initial value A and an exponential growth factor of 22%.
Let's analyze each option:
A. Y = A(0.22)^x
This option is incorrect because the exponential growth factor is less than 1. An exponential growth factor should be greater than 1 to represent growth, but in this case, it is less than 1.
B. Y = A(0.68)^x
This option is also incorrect because the exponential growth factor of 0.68 is less than 1. Similar to option A, the growth factor should be greater than 1 to represent growth.
C. Y = A(1.22)^x
This option is the correct answer. The exponential growth factor of 1.22 is greater than 1, representing an increase. By multiplying the initial value A by 1.22 raised to the power of x, we achieve the desired effect of a 22% annual increase.
D. Y = A(1.68)^x
This option is incorrect because the exponential growth factor of 1.68 is greater than 1. While it represents growth, it is not specifically the 22% increase mentioned in the question.
Therefore, the correct answer is: C. Y = A(1.22)^x, which represents an initial population that increases 22% per year.
Remember, when approaching questions like these, it's important to understand the terminology and concepts involved. In this case, recognizing the need for an exponential growth factor greater than 1 and the specific growth rate mentioned (22%) helped us identify the correct answer.