Question

Joshua had 1000 in his savings account at the endJoshua had $1.000 in his savings account at the end of the year 2020. The function ((%) = 1000(1.16) ^x/3 represents the amount in his savings account x years since 2020. Use the properties of exponents to rewrite the function to reveal the annual growth factor. What is the annual growth factor? Find and describe the constant percentage rate of change.

Answer 1

The Expotenntial Growth factor is 1.16, representing a 16% increase each year in Joshua's savings account.

Step-by-step explanation:

The given function ((%) = 1000(1.16) ^x/3) represents the amount in Joshua's savings account x years since 2020. To reveal the annual growth factor, we can rewrite the function using the properties of exponents. We know that any number raised to the power of 1 is the same number itself. So, we can rewrite the function as:

((%) = 1000(1.16) ^(x/3 * 3/1))

Simplifying, we get:

((%) = 1000(1.16) ^(x))

Therefore, the annual growth factor is 1.16, which represents a 16% increase each year in Joshua's savings account.

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