1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
lilavasa [31]
3 years ago
13

If $6500 is invested at a rate of 6% compounded continuously, find the balance in the account after 3 years

Mathematics
1 answer:
Alex787 [66]3 years ago
6 0

\bf ~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$6500\\ r=rate\to 6\%\to \frac{6}{100}\dotfill &0.06\\ t=years\dotfill &3 \end{cases} \\\\\\ A=6500e^{0.06\cdot 3}\implies A=6500e^{0.18}\implies A\approx 7781.91

You might be interested in
What is the value of the expression 0.6 x 0.8? Solve for the answer using an area mode
KiRa [710]

Step-by-step explanation:

0.6m×0.8

=0.48m²

is like this?

hope it help

5 0
2 years ago
(3/2)^2÷(1-3/2+√(1/8+7/16))×(1+2/3)^3<br> ayudaaaaaaaa
hram777 [196]

Answer:

ayuda wala pa kmi SAP UMAYS

4 0
2 years ago
A number, y, is five times another number, x. The sum of the two numbers is 42. Write the system of equations.
vovikov84 [41]

Answer:

5x+x=42

6x=42

x=7

Step-by-step explanation:

5 0
2 years ago
Read 2 more answers
y′′ −y = 0, x0 = 0 Seek power series solutions of the given differential equation about the given point x 0; find the recurrence
sukhopar [10]

Let

\displaystyle y(x) = \sum_{n=0}^\infty a_nx^n = a_0 + a_1x + a_2x^2 + \cdots

Differentiating twice gives

\displaystyle y'(x) = \sum_{n=1}^\infty na_nx^{n-1} = \sum_{n=0}^\infty (n+1) a_{n+1} x^n = a_1 + 2a_2x + 3a_3x^2 + \cdots

\displaystyle y''(x) = \sum_{n=2}^\infty n (n-1) a_nx^{n-2} = \sum_{n=0}^\infty (n+2) (n+1) a_{n+2} x^n

When x = 0, we observe that y(0) = a₀ and y'(0) = a₁ can act as initial conditions.

Substitute these into the given differential equation:

\displaystyle \sum_{n=0}^\infty (n+2)(n+1) a_{n+2} x^n - \sum_{n=0}^\infty a_nx^n = 0

\displaystyle \sum_{n=0}^\infty \bigg((n+2)(n+1) a_{n+2} - a_n\bigg) x^n = 0

Then the coefficients in the power series solution are governed by the recurrence relation,

\begin{cases}a_0 = y(0) \\ a_1 = y'(0) \\\\ a_{n+2} = \dfrac{a_n}{(n+2)(n+1)} & \text{for }n\ge0\end{cases}

Since the n-th coefficient depends on the (n - 2)-th coefficient, we split n into two cases.

• If n is even, then n = 2k for some integer k ≥ 0. Then

k=0 \implies n=0 \implies a_0 = a_0

k=1 \implies n=2 \implies a_2 = \dfrac{a_0}{2\cdot1}

k=2 \implies n=4 \implies a_4 = \dfrac{a_2}{4\cdot3} = \dfrac{a_0}{4\cdot3\cdot2\cdot1}

k=3 \implies n=6 \implies a_6 = \dfrac{a_4}{6\cdot5} = \dfrac{a_0}{6\cdot5\cdot4\cdot3\cdot2\cdot1}

It should be easy enough to see that

a_{n=2k} = \dfrac{a_0}{(2k)!}

• If n is odd, then n = 2k + 1 for some k ≥ 0. Then

k = 0 \implies n=1 \implies a_1 = a_1

k = 1 \implies n=3 \implies a_3 = \dfrac{a_1}{3\cdot2}

k = 2 \implies n=5 \implies a_5 = \dfrac{a_3}{5\cdot4} = \dfrac{a_1}{5\cdot4\cdot3\cdot2}

k=3 \implies n=7 \implies a_7=\dfrac{a_5}{7\cdot6} = \dfrac{a_1}{7\cdot6\cdot5\cdot4\cdot3\cdot2}

so that

a_{n=2k+1} = \dfrac{a_1}{(2k+1)!}

So, the overall series solution is

\displaystyle y(x) = \sum_{n=0}^\infty a_nx^n = \sum_{k=0}^\infty \left(a_{2k}x^{2k} + a_{2k+1}x^{2k+1}\right)

\boxed{\displaystyle y(x) = a_0 \sum_{k=0}^\infty \frac{x^{2k}}{(2k)!} + a_1 \sum_{k=0}^\infty \frac{x^{2k+1}}{(2k+1)!}}

4 0
2 years ago
Select the correct answer <br> Which is the correct graph for the function <br> F(x)=x+3/x^2-1
Anna11 [10]

Answer:

B i think

Step-by-step explanation:

4 0
3 years ago
Other questions:
  • If the mean of 4,8 and x is 7 what is the value of x
    11·1 answer
  • Find AC,AB=9x+1 BC=6x+25
    15·1 answer
  • X - у - 2z = -6<br> 3х + 2y = -25<br> —4х + у — z = 12
    7·1 answer
  • 1/3 x=5/12 show your work
    6·1 answer
  • HELP ASAP 25 POINTS WILL MARK CORRECT ANSWER BRAINLIEST
    8·1 answer
  • A group of men and women were given a maze puzzle
    13·2 answers
  • A dozen oranges $2.00. How many oranges can be bought for $10.00?
    5·2 answers
  • 432 oranges are to be divided equally among a number of people. If there had been four people less, the share of each would have
    9·1 answer
  • 1-4
    13·1 answer
  • Please help ASAP
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!