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Anton [14]
3 years ago
8

Karen deposited $5,000 as a certificate of deposit (CD) in a bank for a period of 3 years. The CD pays simple interest of 15% pe

r year and pays interest every 6 months. How much interest does she get every 6 months?
$

(Hint: Use the formula i = prt, where i is the interest earned, p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.)
Mathematics
1 answer:
Serhud [2]3 years ago
3 0
375 every 6 months ..........
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A typical cup of coffee contains about 100 mg of caffeine and every hour approximately 16% ofthe amount of caffeine inthe body i
Over [174]

Answer:

a) \frac{dC}{dt} = rC

And for this case we can rewrite the model like this:

\frac{dC}{C} = r dt

If we integrate both sides we got:

ln C = rt + k

If we use exponentials for both sides we got:

C = e^{rt} e^k = C_o e^{rt}

For this case C_o = 100 mg and r = -0.16

So then our model would be given by:

C(t) = 100 e^{-0.16 t}

Where t represent the number of hours

b) C(5) = 100 e^{-0.16*5}= 44.9329

Step-by-step explanation:

Part a

For this case we can assume the proportional model given by:

\frac{dC}{dt} = rC

And for this case we can rewrite the model like this:

\frac{dC}{C} = r dt

If we integrate both sides we got:

ln C = rt + k

If we use exponentials for both sides we got:

C = e^{rt} e^k = C_o e^{rt}

For this case C_o = 100 mg and r = -0.16

So then our model would be given by:

C(t) = 100 e^{-0.16 t}

Where t represent the number of hours

Part b

For this case we can replace the value t=5 into the model and we got:

C(5) = 100 e^{-0.16*5}= 44.9329

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Which value of x makes the equation true? x – 5.1 = –7.6
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X-5.1 = -7.6
 +5.1    +5.1
X= -2.5
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