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Juana invests $1,500 in an account accumulating 3% interest according to the equation v=1500(1.03)^y, where v
represents the value of the account after y years. Marquez and Calvin invest the same amount of money at the same
rate. Marquez invests three years before Juana, and Calvin invests two years after Juana. By what factor would
Calvin's investment need to be increased to equal Marquez's investment at any time after Calvin's investment is
made?

A. 86.3%
B. 97.1%
C. 115.0%
D. 115.9%

Respuesta :

raphealnwobi

Calvin's investment need to be increased by a factor of 115.9% to equal Marquez's investment at any time after Calvin's investment is made.

What is an exponential function?

An exponential function is in the form:

y = abˣ

Where a is the initial value of y and b is the multiplication factor.

Let v represent the value of the account after y years. Hence:

For Juana:

[tex]v=1500(1.03)^y[/tex]

Marquez invests three years before Juana,  Hence:

[tex]v'=1500(1.03)^{y+3}=1500(1.03)^y(1.03)^3=(1.03)^3*v=1.092727v[/tex]

Calvin invests two years after Juana. Hence:

[tex]v"=1500(1.03)^{y-2}=1500(1.03)^y*(1.03)^{-2}=(1.03)^{-2}v[/tex]

v' / v" = ((1.03)³ * v) / ((1.02⁻²) * v) = 1.159 = 115.9%

Calvin's investment need to be increased by a factor of 115.9% to equal Marquez's investment at any time after Calvin's investment is made.

Find out more on exponential function at: https://brainly.com/question/12940982

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