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Alexis put $2000 in a savings account. After 4 years, she had $2543 in the account. What rate of interest did she earn? Use the formula A = Pert, where A is the ending amount, P is the principal (initial amount), r is the interest rate, and t is time.

Respuesta :

apologiabiology
alrighty

P=2000
A=2543
t=4

[tex]A=Pe^{rt}[/tex]
[tex]2543=2000e^{4r}[/tex]
solve

[tex]2543=2000e^{4r}[/tex]

divide both sides by 2000

[tex]\frac{2543}{2000}=e^{4r}[/tex]

take ln of both sides

[tex]ln(\frac{2543}{2000})=ln(e^{4r})[/tex]

[tex]ln(\frac{2543}{2000})=(4r)ln(e)[/tex]

[tex]ln(\frac{2543}{2000})=(4r)(1)[/tex]

[tex]ln(\frac{2543}{2000})=4r[/tex]

divide both sides by 4

[tex]\frac{ln(\frac{2543}{2000})}{4}=r[/tex]

use your calculator

0.060049=r
convert to percent
that is about 6%

the interest rate is 6%

6% just did it on a p e x

Step-by-step explanation:

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