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Trava [24]
3 years ago
9

You invest $2,600 in an account that

Mathematics
1 answer:
SashulF [63]3 years ago
4 0

Answer:

$3,927.53

Step-by-step explanation:

You are going to want to use the continuous compound interest formula, which is shown below.

A = Pe^{rt}

<em>P = principal amount</em>

<em>r = interest rate (decimal)</em>

<em>t = time (years)</em>

<em />

First change 8.25% to its decimal form:

8.25% -> \frac{8.25}{100} -> 0.0825

Next, plug in the values into the equation:

A=2,600e^{0.0825(5)}

A=3,927.53

The balance of the account after 5 years will be $3,927.53

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Suppose after 2500 years an initial amount of 1000 grams of a radioactive substance has decayed to 75 grams. What is the half-li
krok68 [10]

Answer:

The correct answer is:

Between 600 and 700 years (B)

Step-by-step explanation:

At a constant decay rate, the half-life of a radioactive substance is the time taken for the substance to decay to half of its original mass. The formula for radioactive exponential decay is given by:

A(t) = A_0 e^{(kt)}\\where:\\A(t) = Amount\ left\ at\ time\ (t) = 75\ grams\\A_0 = initial\ amount = 1000\ grams\\k = decay\ constant\\t = time\ of\ decay = 2500\ years

First, let us calculate the decay constant (k)

75 = 1000 e^{(k2500)}\\dividing\ both\ sides\ by\ 1000\\0.075 = e^{(2500k)}\\taking\ natural\ logarithm\ of\ both\ sides\\In 0.075 = In (e^{2500k})\\In 0.075 = 2500k\\k = \frac{In0.075}{2500}\\ k = \frac{-2.5903}{2500} \\k = - 0.001036

Next, let us calculate the half-life as follows:

\frac{1}{2} A_0 = A_0 e^{(-0.001036t)}\\Dividing\ both\ sides\ by\ A_0\\ \frac{1}{2} = e^{-0.001036t}\\taking\ natural\ logarithm\ of\ both\ sides\\In(0.5) = In (e^{-0.001036t})\\-0.6931 = -0.001036t\\t = \frac{-0.6931}{-0.001036} \\t = 669.02 years\\\therefore t\frac{1}{2}  \approx 669\ years

Therefore the half-life is between 600 and 700 years

5 0
2 years ago
CAN ANYONE HELP ME ANSWER THIS ​
azamat

Answer:

9/100

Step-by-step explanation:

There are 10 marbles in the bag

There are 3 pink marbles.

P (1st marble pink) = pink marbles/ total marbles

                              = 3/10

We put the marble back.

There are 10 marbles in the bag

There are 3 pink marbles.

P (2nd marble pink) = pink marbles/ total marbles

                                      = 3/10

Multiply the probabilities together

P (pink, then pink) = 3/10 * 3/10 = 9/100

7 0
2 years ago
Find the indicated term of the sequence whose nth term is given by the formula.
Kruka [31]

Answer:

a 12= − 3 n 2 − n

Step-by-step explanation:

3 0
2 years ago
Need help with this
maw [93]

Answer:

0, 5/4

Step-by-step explanation:

If k=0, you get 0=0, which is obviously true.

As long as K is not 0, you can divide by k and get 4k=5 which is solved by k=5/4

6 0
3 years ago
The price of a DVD is $24.00 plus 8% sales tax. What is the sales tax on this DVD in dollars and cents?
Aleonysh [2.5K]

Answer:

3.50 is the right answer

Step-by-step explanation:

4 0
3 years ago
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