We appreciate your visit to You ve set a goal of having tex 10 000 tex after 15 years If you estimate that your investment account will have an average. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
We want to have \[tex]$10,000 after 15 years with an average yearly growth factor of 1.09. This means that if you invest an amount \$[/tex][tex]\(x\)[/tex] today, it will grow to
[tex]$$
x(1.09)^{15}
$$[/tex]
after 15 years. Since you want this amount to be \[tex]$10,000, we set up the equation
$[/tex][tex]$
10000 = x(1.09)^{15}.
$[/tex][tex]$
This is the equation that shows the relationship between the present investment \$[/tex][tex]\(x\)[/tex] and the future amount.
To find out how much to invest today, solve for \[tex]$\(x\) by dividing both sides of the equation by \((1.09)^{15}\):
$[/tex][tex]$
x = \frac{10000}{(1.09)^{15}}.
$[/tex][tex]$
Evaluating this expression gives approximately \$[/tex]2745.38.
Among the provided multiple-choice options:
a. [tex]\(y = 10000(1.09)^5\)[/tex]
b. [tex]\(y = 10000(0.09)^{10}\)[/tex]
c. [tex]\(10000 = x(1.09)^{15}\)[/tex]
d. [tex]\(10000 = x(0.09)\)[/tex],
option c is the one that correctly represents the relationship, so the correct answer corresponds to option c.
[tex]$$
x(1.09)^{15}
$$[/tex]
after 15 years. Since you want this amount to be \[tex]$10,000, we set up the equation
$[/tex][tex]$
10000 = x(1.09)^{15}.
$[/tex][tex]$
This is the equation that shows the relationship between the present investment \$[/tex][tex]\(x\)[/tex] and the future amount.
To find out how much to invest today, solve for \[tex]$\(x\) by dividing both sides of the equation by \((1.09)^{15}\):
$[/tex][tex]$
x = \frac{10000}{(1.09)^{15}}.
$[/tex][tex]$
Evaluating this expression gives approximately \$[/tex]2745.38.
Among the provided multiple-choice options:
a. [tex]\(y = 10000(1.09)^5\)[/tex]
b. [tex]\(y = 10000(0.09)^{10}\)[/tex]
c. [tex]\(10000 = x(1.09)^{15}\)[/tex]
d. [tex]\(10000 = x(0.09)\)[/tex],
option c is the one that correctly represents the relationship, so the correct answer corresponds to option c.
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