4 the equation for compound interest is $a = p(1+\frac{r}{n})^{nt}$ where $p$ is the initial amount…

4 the equation for compound interest is $a = p(1+\frac{r}{n})^{nt}$ where $p$ is the initial amount invested, $r$ is the interest rate as a decimal, $n$ is the number of times compounded annually, and $t$ is the number of years. determine the value of the account if the initial investment is $8,000 compounded monthly at a rate of 6% after 10 years. a. $8409.12 b. $8480.00 c. $14326.78 d. $14555.17 5 esther purchased a used car, a ford focus, for $8400. the car is expected to decrease in value by 20% per year. if the trend continues how much would the car be worth 6 years after esther purchased the car? $y = a(1pm r)^{x}$ $y = 8400(1 - 0.20)^{6}$ 2202.00 6 freddie purchased a pair of never - worn vintage 1997 nike air jordan xii playoff black varsity shoe size 12 for $380. the shoes have shown an average growth rate of 14% per year. if the trend continues how much would the shoes be worth 5 years after freddie purchased the shoes? $y = a(1 + r)^{x}$ $y = 380(1+0.14)^{5}$ 731.66 7 determine the value of an account in which a person invested $6000 for 12 years at an annual rate of 9% compounded quarterly ($n = 4$). $y = a(1+\frac{r}{n})^{ncdot t}$ 8 solve the equation. $2^{3x + 1}=128$ a. $x = 1$ b. $x = 2$ c. $x = 7$ d. $x = 21$

4 the equation for compound interest is $a = p(1+\frac{r}{n})^{nt}$ where $p$ is the initial amount invested, $r$ is the interest rate as a decimal, $n$ is the number of times compounded annually, and $t$ is the number of years. determine the value of the account if the initial investment is $8,000 compounded monthly at a rate of 6% after 10 years. a. $8409.12 b. $8480.00 c. $14326.78 d. $14555.17 5 esther purchased a used car, a ford focus, for $8400. the car is expected to decrease in value by 20% per year. if the trend continues how much would the car be worth 6 years after esther purchased the car? $y = a(1pm r)^{x}$ $y = 8400(1 - 0.20)^{6}$ 2202.00 6 freddie purchased a pair of never - worn vintage 1997 nike air jordan xii playoff black varsity shoe size 12 for $380. the shoes have shown an average growth rate of 14% per year. if the trend continues how much would the shoes be worth 5 years after freddie purchased the shoes? $y = a(1 + r)^{x}$ $y = 380(1+0.14)^{5}$ 731.66 7 determine the value of an account in which a person invested $6000 for 12 years at an annual rate of 9% compounded quarterly ($n = 4$). $y = a(1+\frac{r}{n})^{ncdot t}$ 8 solve the equation. $2^{3x + 1}=128$ a. $x = 1$ b. $x = 2$ c. $x = 7$ d. $x = 21$

Answer

4.

Explanation:

Step1: Identify values

$P = 8000$, $r=0.06$, $n = 12$, $t = 10$

Step2: Substitute into compound - interest formula

$A=P(1 +\frac{r}{n})^{nt}=8000(1+\frac{0.06}{12})^{12\times10}$

Step3: Calculate the value inside the parentheses

$1+\frac{0.06}{12}=1 + 0.005=1.005$

Step4: Calculate the exponent

$12\times10 = 120$

Step5: Calculate the power

$1.005^{120}\approx1.819396734$

Step6: Multiply by the principal

$A = 8000\times1.819396734\approx14555.17$

Answer:

d. $$14,555.17$

5.

Explanation:

Step1: Identify values

$a = 8400$, $r=0.2$, $x = 6$

Step2: Substitute into the depreciation formula

$Y=a(1 - r)^{x}=8400(1 - 0.2)^{6}$

Step3: Calculate inside the parentheses

$1-0.2 = 0.8$

Step4: Calculate the power

$0.8^{6}=0.262144$

Step5: Multiply by the initial value

$Y=8400\times0.262144 = 2202.01$ (approx. $2202.00$)

Answer:

$2202.00$

6.

Explanation:

Step1: Identify values

$a = 380$, $r = 0.14$, $x=5$

Step2: Substitute into the growth formula

$Y=a(1 + r)^{x}=380(1 + 0.14)^{5}$

Step3: Calculate inside the parentheses

$1+0.14 = 1.14$

Step4: Calculate the power

$1.14^{5}\approx1.92541577$

Step5: Multiply by the initial value

$Y=380\times1.92541577\approx731.66$

Answer:

$731.66$

7.

Explanation:

Step1: Identify values

$a = 6000$, $r=0.09$, $n = 4$, $t = 12$

Step2: Substitute into compound - interest formula

$y=a(1+\frac{r}{n})^{nt}=6000(1+\frac{0.09}{4})^{4\times12}$

Step3: Calculate the value inside the parentheses

$1+\frac{0.09}{4}=1+0.0225 = 1.0225$

Step4: Calculate the exponent

$4\times12=48$

Step5: Calculate the power

$1.0225^{48}\approx2.93283797$

Step6: Multiply by the principal

$y=6000\times2.93283797\approx17597.03$

8.

Explanation:

Step1: Rewrite 128 as a power of 2

$128 = 2^{7}$, so the equation $2^{3x + 1}=128$ becomes $2^{3x + 1}=2^{7}$

Step2: Set the exponents equal

$3x+1 = 7$

Step3: Solve for x

Subtract 1 from both sides: $3x=7 - 1=6$ Divide both sides by 3: $x = 2$

Answer:

b. $x = 2$