The constant percent rate of change for the function g(x) is option (D) 2% is the correct answer.
Compound interest is the interest you earn on interest. Compound interest is the interest calculated on the principle and the interest accumulated over the previous period.
For the given situation,
The function [tex]g(x) = 500(1.02)^x -------- (1)[/tex]
Principle = $500
Number of years, T = x
The formula of amount in compound interest is
[tex]A=p(1+\frac{r}{n} )^{nT}[/tex]
Interest is compounded annually, so n=1
⇒ [tex]A=p(1+r)^{T} ------ (2)[/tex]
On comparing equation 1 and 2,
⇒ [tex]1.02=1+r[/tex]
⇒ [tex]r=1.02-1[/tex]
⇒ [tex]r=0.02[/tex]
Rate of interest should be in percentage,
⇒ [tex]0.02(100\%)[/tex]
⇒ [tex]2\%[/tex]
Hence we can conclude that the constant percent rate of change for the function g(x) is option (D) 2% is the correct answer.
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