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3 years ago

Jake’s bank offers him an account with 3% interest, compounded

1 answer:

defon3 years ago

6 0

$\bf \qquad \textit{Compound Interest Earned Amount}
\\\\
A=P\left(1+\frac{r}{n}\right)^{nt}
\quad 
\begin{cases}
A=\textit{compounded amount}\\
P=\textit{original amount deposited}\to &\$1320\\
r=rate\to 3\%\to \frac{3}{100}\to &0.03\\
n=
\begin{array}{llll}
\textit{times it compounds per year}\\
\textit{annually, meaning once}
\end{array}\to &1\\

t=years\to &5
\end{cases}$

he'll be earning in interest, the difference from A to P, or A - P

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Samantha puts an initial $500 into a savings account. The account has a 4% annual compound interest rate. What is the function t

Licemer1 [7]

I use a bit of a different looking formula.

A(t)=P(1+r/n)^nt

P=amount of money. (500)
r= rate (in decimal. 4%=0.04)
n=number of times per year (1 in this problem)
t=amount of time. (5 years)

Plugged in it looks like this:

A(t)=500 (1+ 0.04/1)^1x5

Then I put it into my calculator like this:

0.04/1+ 0.04

Then add one to the above answer:

0.04+1=1.04

Then raise the above answer to the 1x5:

1.04^5=1.2166......

Then multiply the above answer by 500:

1.2166.... x 500=608.3264512

She has $608 after 5 years.

Hope this helps, let me know if you have any questions.

5 0

3 years ago

Joseph has 10 wooden boards, each is 2 meters in length. he needs 8 yards of wood to repair his fence and 25 feet to make shelve

Molodets [167]

Answer:

the answer is A he can complete both projects.

Step-by-step explanation:

3 0

3 years ago

What is x²+x-30 as a binomial?

Zolol [24]

X^2+x-30 -- find two numbers that add to one and multiply to -30, which would be 6 and -5. so now you have x^2+6x-5x-30. factor out x and 5 to get x(x+6)-5(x+6). so you get (x+6)*(x-5)

6 0

3 years ago

Read 2 more answers

A cylinder has a volume of 198 and base has an area of 22 what is the height o the cylinder

Mumz [18]

Answer:

Step-by-step explanation:

The base of the cylinder is in the shape of a circle:

Area of the base= $\pi *r^2$

For Base area=22 square units

$22=\pi *r^2$

$22=3.14*r^2\\r^2=22/3.14\\r^2=7.01\\r=\sqrt{7.01}$

Volume of the cylinder= $\pi *r^2*h$

For volume '198 cubic units' the height(h) is:

$198=\pi *r^2*h$

$198=3.14*(\sqrt{7.01})^2*h$

$198=3.14*7.01*h\\\\198=22.01*h\\\\198/22.01=h\\\\h=9 units\\$

4 0

3 years ago

The government of the Republic of Lemon Island plans to transform their lemon-based economy into a tourism-based economy. They d

NNADVOKAT [17]

Step-by-step explanation:

dy/dt = (A − Be^(-t/5)) y

(a) First, find the general solution by separating the variables and integrating.

dy / y = (A − Be^(-t/5)) dt

dy / y = [A + 5B (-⅕ e^(-t/5))] dt

ln |y| = At + 5B e^(-t/5) + C

y = e^(At + 5B e^(-t/5) + C)

y = Ce^(At + 5B e^(-t/5))

Given that A = 0.06, B = 0.04, and y(0) = 50×10⁶ − 10×10⁶ = 40×10⁶:

40×10⁶ = Ce^(0.06(0) + 5(0.04) e^(-0/5))

40×10⁶ = Ce^(0.2)

C = 40×10⁶ e^(-0.2)

y = 40×10⁶ e^(-0.2) e^(0.06t + 0.2 e^(-t/5))

y = 40×10⁶ e^(-0.2 + 0.06t + 0.2 e^(-t/5))

(b) If A = 0.02 and B = 0, and there is no transformation (y(0) = 50×10⁶), then:

50×10⁶ = Ce^(0.02(0) + 0)

50×10⁶ = C

y = 50×10⁶ e^(0.02t)

Comparing to the answer from part (a):

40×10⁶ e^(-0.2 + 0.06t + 0.2 e^(-t/5)) = 50×10⁶ e^(0.02t)

e^(-0.2 + 0.04t + 0.2 e^(-t/5)) = 5/4

-0.2 + 0.04t + 0.2 e^(-t/5) = ln(5/4)

-5 + t + 5e^(-t/5) = 25 ln(5/4)

t + 5e^(-t/5) = 5 + 25 ln(5/4)

Solve with a calculator:

t = 9.886

The transformed economy surpasses the untransformed economy in the 10th year.

y = 40×10⁶ e^(-0.2 + 0.06(5) + 0.2 e^(-5/5))

y = 47.6×10⁶

The percent growth is:

(47.6×10⁶ − 40×10⁶) / 40×10⁶ × 100% = 19%

The growth rate is greater than 4%, so the current government can expect to be reelected.

3 0

3 years ago