Question

mateo bought a grand piano for $5,010.25. the piano increases in value by 1.99% each year. which equation can be used to find the number of years it will take for the piano to be worth twice the original purchase price? a. 10,020.50 = 5,010.25(1 + 1.99)^t b. 5,010.25 = 10,020.50(1 + 1.99)^t c. 5,010.25 = 10,020.50(1 + 0.0199)^t d. 10,020.50 = 5,010.25(1 + 0.0199)^t

Explanation:

Step1: Identify compound growth formula

The compound growth formula is $A = P(1 + r)^t$, where $A$ is final amount, $P$ is principal, $r$ is growth rate, $t$ is time.

Step2: Define values for the problem

Original price $P = 5010.25$, final amount $A = 2\times5010.25 = 10020.50$, growth rate $r = 0.0199$.

Step3: Substitute values into formula

Substitute $A$, $P$, $r$ into the growth formula:
$10020.50 = 5010.25(1 + 0.0199)^t$

Answer:

D. $10,020.50 = 5,010.25(1 + 0.0199)^t$