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KengaRu [80]
3 years ago
15

$6,700 is invested in an account earning 8. 3% interest (APR), compounded daily. Write a function showing the value of the accou

nt after t years, where the annual growth rate can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage of growth per year (APY), to the nearest hundredth of a percent
Mathematics
1 answer:
aliina [53]3 years ago
7 0

Answer:

  A = $6,700(1 +0.0865^t)

  APY = 8.65%

Step-by-step explanation:

Daily compounding of interest results in an annual growth factor of ...

  gf = (1 +r/365)^365 . . . . for APR = r

Your growth factor is ...

  gf = (1 +0.083/365)^365 ≈ 1.086532

Then the growth rate (APY) is ...

  APY = gf -1 ≈ 8.65%

The account value is multiplied by the growth factor each year, so after t years will be ...

  A = P(1 +APY)^t

  A = $6,700(1 +0.0865)^t . . . . . . . 0.0865 is the annual growth rate

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3 years ago
At Clucker's Chicken, a bucket of 4 pieces of dark meat and 5 pieces of white meat costs 7.05. A bucket of 3 pieces of dark meat
Alenkinab [10]

Answer:

The cost of a piece of dark meat is <u>$0.70</u> and the cost of a piece of white meat is <u>$0.85</u>.

Step-by-step explanation:

Given:

At Clucker's Chicken, a bucket of 4 pieces of dark meat and 5 pieces of white meat costs 7.05.

A bucket of 3 pieces of dark meat and 8 pieces of white meat costs 8.90.

Now, to find the cost of a piece of dark meat and the cost of a piece of white meat.

Let the cost of a piece of dark meat be x.

And the cost of a piece of white meat be y.

A bucket of 4 pieces of dark meat and 5 pieces of white meat costs $7.05.

So,

4x+5y=7.05

4x=7.05-5y  

x=\frac{7.05-5y}{4}   .......(1)

Now, a bucket of 3 pieces of dark meat and 8 pieces of white meat costs $8.90.

3x+8y=8.90

Substituting the value of x from equation (1) we get:

3(\frac{7.05-5y}{4})+8y=8.90

\frac{21.15-15y}{4} +8y=8.90

\frac{21.15-15y+32y}{4} =8.90

<em>Multiplying both sides by 4 we get:</em>

21.15-15y+32y=35.60

21.15+17y=35.60

<em>Subtracting both sides by 21.15 we get:</em>

17y=14.45

<em>Dividing both sides by 17 we get:</em>

y=0.85

<u>The cost of a piece of white meat = $0.85.</u>

Now, substituting the value of y in equation (1) we get:

x=\frac{7.05-5y}{4}

x=\frac{7.05-5\times 0.85}{4}

x=\frac{7.05-4.25}{4}

x=\frac{2.8}{4}

x=0.70.

<u>The cost of a piece of dark meat = $0.70.</u>

Therefore, the cost of a piece of dark meat is <u>$0.70</u> and the cost of a piece of white meat is <u>$0.85</u>.

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