Find the annual percent increase or decrease that y = 0.35(2.3)x models. (1 point) A.230% increase B.130% increase C.30% decrease D.65% decrease

If x represents the number of years, we have to determine the two values of y in consecutive terms to determine if the value of y increases or decreases after a year.

This function is equivalent to the exponential growth function

[tex]y=A(1+r)^x[/tex], where A=0.35 and (1+r)=2.3, [A= initial amount , r=annual percent increase]

Thus,

[tex]\Rightarrow\ r=2.3-1\\\Rightarrow\ r=1.3\\\Rightarrow\ r=1.3\times100\%=130\%[/tex]

Hence, the annual percent increase is 130%.

AkshayG AkshayG · Answer 2 · 2019-10-20T21:10:51+02:00

The annual percent of the model [tex]y = 0.35{\left( {2.3}\right)^x}[/tex] is increases by [tex]\boxed{130\% }[/tex]. Option (B) is correct.

Further explanation:

The exponential growth function or compound interest formula can be expressed as follows,

[tex]\boxed{A = C{{\left( {1 + i} \right)}^x}}[/tex]

Here, A represents the total amount, C represents the initial amount, irepresent the annual percentage increase and x represents the time.

Given:

The annual percentage model can be expressed as,

[tex]y = 0.35{\left( {2.3} \right)^x}[/tex]

The options of annual percentage are given as follows.

A. [tex]230\% {\text{ increases}}.[/tex]

B. [tex]130\% {\text{ increases}}.[/tex]

C. [tex]30\% {\text{ decreases}}.[/tex]

D. [tex]65\% {\text{ decreases}}.[/tex]

Explanation:

Compare given model [tex]y = 0.35{\left( {2.3} \right)^x}[/tex] with the exponent growth model [tex]y = 0.35{\left( {2.3}\right)^x}.[/tex]

The value of C is 0.35 and the value of [tex]\left( {1 + i} \right)[/tex] is 2.3.

[tex]\begin{aligned}1 + i&= 2.3\\i &=2.3 - 1\\i &= 1.3\\\end{aligned}[/tex]

The function is increases by [tex]130\%.[/tex]

Option A is not correct.

Option B is correct.

Option C is not correct.

Option D is not correct.

Hence, the annual percent of the model [tex]y = 0.35{\left( {2.3}\right)^x}[/tex] is increases by [tex]\boxed{130\% }[/tex]. Option (B) is correct.

Learn more:

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Answer details:

Grade: High School

Subject: Mathematics

Chapter: Investment

Keywords: Annual percentage, increases or decreases, model, interest rate, simple interest, compound interest, annual payment, annuity.