Jenny invests 2 dollars comma 000 at an interest rate of 5 percent The amount of money, m sub A , in Jenny’s account after t years can be represented using the equation m sub A is equal to 2000 times 1 point 0 5 to the t th power If Jenny would have invested the same amount of money at the same interest rate four years ago, the equation representing the amount of money, m sub b , in her account would be represented using the equation m sub b is equal to 2000 times 1 point 0 5 raised to the t plus 4 power Which of the following is equivalent to m sub b ?
Answer
A
m sub b is equal to the fraction with numerator 2000 times 1 point 0 5 to the t th power and denominator 1 point 0 5 to the 4th power
B
m sub b is equal to 2000 times 1 point 0 5 to the t th power plus 1 point 0 5 to the 4th power
C
m sub b is equal to 2000 1 point 0 5 to the t th power 1 point 0 5 to the 4th power
D
m sub b is equal to the fraction with numerator 2000 times 1 point 0 5 to the 4th power and denominator 1 point 0 5 to the t th power
Explanation
Use the exponent rule that a base raised to a sum can be split into a product: 1.05^(t + 4) = 1.05^t × 1.05^4. Therefore, m_b = 2000 × 1.05^t × 1.05^4, which is choice C. Choice A divides by 1.05^4, so it does not represent the given expression.
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