Henry begins a savings account with $500. The savings account accumulates 2.5% annual interest based on the equation Vh=500(1.025)^t , where Vh is the value of the account after t years. Andres begins a savings account three years later with the same initial amount of money at the same interest rate. Which equations represent the value of Andres’s account after t years?
A) Va=500(1.025)^t-3 and Va=464.30(1.025)^t
B) Va=500(1.025)^t+3 and Va=538.45(1.025)^t
C)Va=500(1.025)^t-3 and Va=538.45(1.025)^t
D)Va=500(1.025)^t+3 and Va=464.30(1.025)^t

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joaobezerra joaobezerra · Answer 1 · 2022-07-12T19:21:05+02:00

The exponential function that represents the value of Andres’s account after t years is:

A) Va=500(1.025)^t-3 and Va=464.30(1.025)^t

For Henry, it is given by:

[tex]Vh = 500(1.025)^t[/tex]

Andres starts 3 years later than Henry, hence the equation is:

[tex]Va = 500(1.025)^{t - 3}[/tex]

Applying an exponential simplification, we have that:

[tex]Va = 500\frac{1.025^t}{1.025^3} = 464.3(1.025)^t[/tex]

Hence option A is correct.

More can be learned about exponential functions at https://brainly.com/question/25537936

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