Marilyn collects old dolls. She purchases a doll for $450. Research shows this doll's value will increase by 2.5% each year. Write an equation that determines the value, V, of the doll t after purchase.

What we know is that Marilyn purchases a doll for $450 dollars, and the value will increase by 2.5% each year. Now that we know this, this means we need an addition equation. We know 450 is being add to the 2.5% increase so the equation is V = 450 + 0.025t. (I put 2.5% as a decimal (0.025))

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AmitPaswan AmitPaswan · Answer 2 · 2022-06-10T15:38:26+02:00

The equation that determines the value, V, of the doll (t) after purchase is [tex]V = 450 ({1.025}{} )^{t}[/tex]

What is equation?

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

What is compound interest?

Compound interest is an interest accumulated on the principal and interest together over a given time period. The compound interest is calculated, after calculating the total amount over a period of time, based on the rate of interest, and the initial principal.

Formula of Compound Interest

[tex]A = P (1+\frac{r}{100} )^{n}[/tex]

Where,

A = Final amount

P = Initial principal

r = Rate per annum

n = Time in years

According to the question

Marilyn purchases a doll for = $450

i.e, Initial Principal (P) = $450

Doll's value will increase each year by = 2.5%

i.e, Rate per annum = 2.5%

Value (V) of the doll after purchase = Final amount (A)

(t) = Time in years (n)

Now, Formula of compound interest

[tex]A = P (1+\frac{r}{100} )^{n}[/tex]

Substituting the values in formula

[tex]V = 450 (1+\frac{2.5}{100} )^{t}[/tex]

[tex]V = 450 (1+{0.025}{} )^{t}[/tex]

[tex]V = 450 ({1.025}{} )^{t}[/tex].

Hence, equation that determines the value, V, of the doll (t) after purchase is [tex]V = 450 ({1.025}{} )^{t}[/tex]

To know more about compound interest here:

https://brainly.com/question/14295570

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