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bekas [8.4K]
3 years ago
9

If you deposit $1000 in a savings account with an interest rate of r compounded annually, then the balance in the account after

3 years is given by the function B(c)=1000(1+r)^3, where r is written as a decimal. What is the formula for the interest rate, r; required to achieve a balance of B in the account after 3 years?

Mathematics
1 answer:
Sedaia [141]3 years ago
5 0

Answer:

B

Step-by-step explanation:

Our equation is as follows, B(c)=1000(1+r)^3. We are being asked to manipulate the equation and have it be r equals in order to solve for an interest rate when given a balance B. To solve the equation for the variable r, we must isolate r by completing order of operations or PEMDAS backwards.

SADMEP allows us to undo subtraction, addition, and etc in the correct order. We have no subtraction or addition outside of more complex operations. So we move to multiplication or division.

We divide both sides by 1000.

\frac{B}{1000} =\frac{1000(1+r)^{3} }{1000}

We simplify the right side.

\frac{B}{1000} =(1+r)^{3}

We need to now undo the exponent of 3 by using the inverse, a cube root.

\sqrt[3]{\frac{B}{1000}} =\sqrt[3]{(1+r)^{3}}

We simplify the right side.

\sqrt[3]{\frac{B}{1000}} =(1+r)

We subtract 1 to both sides to get r alone.

-1+\sqrt[3]{\frac{B}{1000}} =r

For our last step, we simplify the denominator of the root because 10*10*10=1000.

-1+\frac{\sqrt[3]{b} }{10} =r

This is answer choice b.



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At a certain coffee shop, all the customers buy a cup of coffee; some also buy a doughnut. The shop owner believes that the numb
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Answer:

a) 0.2514

b) No

c) 0.2611

Step-by-step explanation:

For coffee cups sold daily

Mean(μ) = 320 cups

Standard deviation (σ) = 20 cups

For doughnut sold daily

Mean(μ) = 150 doughnut

Standard deviation (σ) = 12 doughnut

Let X be the random variable representing the number of cups.

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Using normal distribution

Z = (x - μ)/σ

Z = (2000 - 6(320))/6(20)

Z = (2000 - 1920) / 120

Z = 80/120

Z = 0.67

From the normal distribution table, 0.67 = 0.2486

Φ(z) = 0.2486

Recall that if Z is positive,

Pr(x>a) = 0.5 - Φ(z)

Pr(x>2000) = 0.5 - 0.2486

= 0.2514

b) On each cup of coffee, he makes a profit of 50 cents and makes a profit of 40 cents on each doughnut. We have 0.5x + 0.4y

Z = (x - μ) / σ

Z = (300 - (0.5*320 + 0.4*150)) / √0.5^2*20^2 + 0.4^2*12^2

Z = (300 - (160+60)) / √100+23.04

Z = (300 -220)/√123.04

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= 7.02

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c) The probability that on any given day he will sell a doughnut to more than half of his coffee customers = Pr(y - 0.5x > 0)

From normal distribution,

Z = (x - μ) / σ

Z = (0 - (150 - 0.5*320)) / √12^2 + 0.5^2*20^2

Z = (0 - (150 - 160)) / √144 + 100

Z = (0 -(-10))/√244

Z = 10/15.62

= 0.64

From the normal distribution table, 0.64 = 0.2389

Φ(z) = 0.2389

Recall that if Z is positive,

Pr(x>a) = 0.5 - Φ(z)

Pr(y - 0.5x >0) = 0.5 - 0.2389

= 0.2611

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