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Marcus has opened a savings account where the yearly interest rate is 10%. He deposits $1,000 to start the account. After t years, the amount of money in the account is modeled by the function An=1,0001+0.10t. Which functions below would be an approximate equivalent function?


Select all that apply.


A. An=1,000(1.10)t

B. An=1,000(1+0.008)^12t

C. An=1,000(1+0.46)^4t

D. An=1,000(1.008)^t/12

E. An=1,000(1.46)^t/4

Sagot :

Answer:

Option A and option B applies

Step-by-step explanation:

The compound interest formula is given by:

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

Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time in years for which the money is invested or borrowed.

Marcus has opened a savings account where the yearly interest rate is 10%. He deposits $1,000 to start the account.

This means, respectively, that: [tex]r = 0.1, P = 1000[/tex]. So

[tex]A(t) = 1000(1 + \frac{0.1}{n})^{nt}[/tex]

Option A:

[tex]n = 1[/tex]. So

[tex]A(t) = 1000(1 + \frac{0.1}{1})^{t}[/tex]

[tex]A(t) = 1000(1.1)^{t}[/tex]

So option A applies

Option B:

[tex]n = 12[/tex]. So

[tex]A(t) = 1000(1 + \frac{0.1}{12})^{12t}[/tex]

0.1/12 = 0.008. So

[tex]A(t) = 1000(1 + 0.008)^{12t}[/tex]

[tex]A(t) = 1000(1.008)^{12t}[/tex]

So option B also applies.

The other options will not apply.

Answer:

A and B

Step-by-step explanation:

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