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4 years ago

3

Mathematics

1 answer:

stiks02 [169]4 years ago

5 0

Answer: $240

Step-by-step explanation:

12 x 8 = 96

96 x $2.50 = 240

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If Tanisha has $1000 to invest at 7% per annum compounded semiannually, how long will it be before she has $1600? If the co

Sphinxa [80]

Answer:

Using continuous interest 6.83 years before she has $1600.

Using continuous compounding, 6.71 years.

Step-by-step explanation:

Compound interest:

The compound interest formula is given by:

$A(t) = P(1 + \frac{r}{n})^{nt}$

Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per unit year and t is the time in years for which the money is invested or borrowed.

Continuous compounding:

The amount of money earned after t years in continuous interest is given by:

$P(t) = P(0)e^{rt}$

In which P(0) is the initial investment and r is the interest rate, as a decimal.

If Tanisha has $1000 to invest at 7% per annum compounded semiannually, how long will it be before she has $1600?

We have to find t for which $A(t) = 1600$ when $P = 1000, r = 0.07, n = 2$

$A(t) = P(1 + \frac{r}{n})^{nt}$

$1600 = 1000(1 + \frac{0.07}{2})^{2t}$

$(1.035)^{2t} = \frac{1600}{1000}$

$(1.035)^{2t} = 1.6$

$\log{1.035)^{2t}} = \log{1.6}$

$2t\log{1.035} = \log{1.6}$

$t = \frac{\log{1.6}}{2\log{1.035}}$

$t = 6.83$

Using continuous interest 6.83 years before she has $1600

If the compounding is continuous, how long will it be?

We have that $P(0) = 1000, r = 0.07$

Then

$P(t) = P(0)e^{rt}$

$1600 = 1000e^{0.07t}$

$e^{0.07t} = 1.6$

$\ln{e^{0.07t}} = \ln{1.6}$

$0.07t = \ln{1.6}$

$t = \frac{\ln{1.6}}{0.07}$

$t = 6.71$

Using continuous compounding, 6.71 years.

7 0

3 years ago

The slant asymptote of f(x)= x^2+3x-3/x+4 is y=x+1

Verdich [7]

Answer:

y=x-1

Step-by-step explanation:

6 0

3 years ago

Sarah earned some money taking care of a dog. She charged $8.50 for washing the dog and $7 for walking the dog. She spent $1.15

Mars2501 [29]

I think the answer would be $13.35

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3 years ago

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The dot plot shows how many swimmers are in each line at a waterpark: Dot plot titled Swimmers in Line and labeled Number of Swi

nasty-shy [4]

The answer is median, because the data is skewed and there is an outlier.

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3 years ago

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Which expression is equivalent to n2 + 26n + 88 for all values of n?

Y_Kistochka [10]

Answer:

(n + 4)(n+ 22)

Step-by-step explanation:

One way to determine which factored expression is accurate is by asking the question: "Which two numbers multiply to 88, but add to 26?" If you are having difficulty using this method, you can always try the guess-and-check method with a multiple choice question. This way involves multiplying the terms inside one set of parentheses with the terms inside the other set of parentheses.

Step #1: Multiply the first terms

(n + 4)(n + 22) ----> n x n = n²

Step #2: Multiply the inside terms

(n + 4)(n + 22) -----> 4 x n = 4n

Step #3: Multiply the outside terms

(n + 4)(n + 22) -----> n x 22 = 22n

Step #4: Multiply the last terms

(n + 4)(n + 22) -----> 4 x 22 = 88

Step #5: Write the new expanded equation and simplify

(n + 4)(n + 22) -----> n² + 4n + 22n + 88 -----> n² + 26n + 88

3 0

2 years ago