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3 years ago

Shelly invested $1,000 at a rate of 5% interest per year. Which equation models the value of the investment, V, after t years?

Mathematics

1 answer:

Nana76 [90]3 years ago

8 0

Answer:

Step-by-step explanation:

You don't say whether this is compound interest or simple interest.

I will assume it's compounding that interests you.

The appropriate formula is

A = P(1 + r)^t, where r is the interest rate as a decimal fraction, t is the time in years, and P is the original amount. Thus:

A = $1000·(1 + 0.05)^t, or A = $1000·(1.05)^t

Please note: There were apparently possible answer choices. Next time, please be sure to list such choices. Thank you.

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The application of scientific knowledge to solve problems or create new products.

Alla [95]

Answer:

The application of scientific knowledge to solve problems or create new products is inter dependant with curiosity

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3 years ago

Read 2 more answers

3. Alexander deposited money into his retirement account that is compounded annually at an interest rate of 7%. Alexander though

Akimi4 [234]

The equation for compound interest is:

Where r is the interest rate and n is the number of times per year it's applied. Annually n = 1 and 7% interest r = 0.07 The quarterly rate 2% is already quartered 0.02 = r/n .

You can see that Alexander is incorrect. A quarterly compound interest rate of 2% will accrue more interest than a 7% compound annual interest rate.

1.7% compound quarterly Hope this helps:)

5 0

3 years ago

Calculus 2. Please help

Anarel [89]

Answer:

$\displaystyle \int\limits^1_0 {\frac{1}{xe^{x^2}}} \, dx = \infty$

General Formulas and Concepts:

Algebra I

Exponential Rule [Rewrite]: $\displaystyle b^{-m} = \frac{1}{b^m}$

Calculus

Limits

Right-Side Limit: $\displaystyle \lim_{x \to c^+} f(x)$

Limit Rule [Variable Direct Substitution]: $\displaystyle \lim_{x \to c} x = c$

Derivatives

Derivative Notation

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Integrals

Definite Integrals

Integration Constant C

Integration Rule [Fundamental Theorem of Calculus 1]: $\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)$

Integration Property [Multiplied Constant]: $\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx$

U-Substitution

U-Solve

Improper Integrals

Exponential Integral Function: $\displaystyle \int {\frac{e^x}{x}} \, dx = Ei(x) + C$

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle \int\limits^1_0 {\frac{1}{xe^{x^2}} \, dx$

Step 2: Integrate Pt. 1

[Integral] Rewrite [Exponential Rule - Rewrite]: $\displaystyle \int\limits^1_0 {\frac{1}{xe^{x^2}} \, dx = \int\limits^1_0 {\frac{e^{-x^2}}{x} \, dx$
[Integral] Rewrite [Improper Integral]: $\displaystyle \int\limits^1_0 {\frac{1}{xe^{x^2}} \, dx = \lim_{a \to 0^+} \int\limits^1_a {\frac{e^{-x^2}}{x} \, dx$

Step 3: Integrate Pt. 2

Identify variables for u-substitution.

Set: $\displaystyle u = -x^2$
Differentiate [Basic Power Rule]: $\displaystyle \frac{du}{dx} = -2x$
[Derivative] Rewrite: $\displaystyle du = -2x \ dx$

Rewrite u-substitution to format u-solve.

Rewrite du: $\displaystyle dx = \frac{-1}{2x} \ dx$

Step 4: Integrate Pt. 3

[Integral] Rewrite [Integration Property - Multiplied Constant]: $\displaystyle \int\limits^1_0 {\frac{1}{xe^{x^2}} \, dx = \lim_{a \to 0^+} -\int\limits^1_a {-\frac{e^{-x^2}}{x} \, dx$
[Integral] Substitute in variables: $\displaystyle \int\limits^1_0 {\frac{1}{xe^{x^2}} \, dx = \lim_{a \to 0^+} -\int\limits^1_a {\frac{e^{u}}{-2u} \, du$
[Integral] Rewrite [Integration Property - Multiplied Constant]: $\displaystyle \int\limits^1_0 {\frac{1}{xe^{x^2}} \, dx = \lim_{a \to 0^+} \frac{1}{2}\int\limits^1_a {\frac{e^{u}}{u} \, du$
[Integral] Substitute [Exponential Integral Function]: $\displaystyle \int\limits^1_0 {\frac{1}{xe^{x^2}} \, dx = \lim_{a \to 0^+} \frac{1}{2}[Ei(u)] \bigg| \limits^1_a$
Back-Substitute: $\displaystyle \int\limits^1_0 {\frac{1}{xe^{x^2}} \, dx = \lim_{a \to 0^+} \frac{1}{2}[Ei(-x^2)] \bigg| \limits^1_a$
Evaluate [Integration Rule - FTC 1]: $\displaystyle \int\limits^1_0 {\frac{1}{xe^{x^2}} \, dx = \lim_{a \to 0^+} \frac{1}{2}[Ei(-1) - Ei(a)]$
Simplify: $\displaystyle \int\limits^1_0 {\frac{1}{xe^{x^2}} \, dx = \lim_{a \to 0^+} \frac{Ei(-1) - Ei(a)}{2}$
Evaluate limit [Limit Rule - Variable Direct Substitution]: $\displaystyle \int\limits^1_0 {\frac{1}{xe^{x^2}} \, dx = \infty$

∴ $\displaystyle \int\limits^1_0 {\frac{1}{xe^{x^2}} \, dx$ diverges.

Topic: Multivariable Calculus

7 0

3 years ago

Fandango has movie tickets on sale for 1\2 price. You buy 2 $12 tickets and you must pay 6% sales tax. What is your total cost a

Colt1911 [192]

Answer:

$12.72 or $25.44

Step-by-step explanation:

if he buys 2 tickets that are $12 each. half of 12 is 6 so you will have to pay 12 plus tax(6%). to find tax you would multiply 12 x .06 which would be $12.72. if it say the tickets are half off from $24 being $12 each then the answer would be $25.44. the question dosent specify that.

hope i helped

8 0

3 years ago

How would I organize the calculation

Viefleur [7K]

Answer:

52 should be the answer

Step-by-step explanation:

first, love the parathesis. subtract 7-2

second 3 raised to the second power

third times 3 raised to the third power by 5 the answer a few u substrates 7-2

fourth 14 divide 2

finally I would add (14/2) 7 + 45 (which is 9 times 5)

read through it carefully by the end if the problem, you should have 52 as the ans

6 0

2 years ago