samantha opened a savings account and deposited $8192. the account earns 10% in interest annually. she makes…

samantha opened a savings account and deposited $8192. the account earns 10% in interest annually. she makes no further deposits and does not withdraw any money. in t years, she has $25,710 in this account. write an equation in terms of t that models the situation.

samantha opened a savings account and deposited $8192. the account earns 10% in interest annually. she makes no further deposits and does not withdraw any money. in t years, she has $25,710 in this account. write an equation in terms of t that models the situation.

Answer

Answer:

$8192(1 + 0.1)^t=25710$

Explanation:

Step1: Identify compound - interest formula

The compound - interest formula is $A = P(1 + r)^t$, where $A$ is the final amount, $P$ is the principal amount, $r$ is the annual interest rate as a decimal, and $t$ is the number of years.

Step2: Identify values given

$P = 8192$, $r=0.1$ (since $10%=0.1$), and $A = 25710$.

Step3: Substitute values into formula

Substitute $P = 8192$, $r = 0.1$, and $A = 25710$ into $A = P(1 + r)^t$ to get $8192(1 + 0.1)^t=25710$.