brainliest answer <br>points question in the photo!!

Use the "rule of 72" to estimate the doubling time (in years) for the interest rate, and then calculate it exactly. (Round your

Law Incorporation [45]

Answer:

According to the rule of 72, the doubling time for this interest rate is 8 years.

The exact doubling time of this amount is 8.04 years.

Step-by-step explanation:

Sometimes, the compound interest formula is quite complex to be solved, so the result can be estimated by the rule of 72.

By the rule of 72, we have that the doubling time D is given by:

$D = \frac{72}{Interest Rate}$

The interest rate is in %.

In our exercise, the interest rate is 9%. So, by the rule of 72:

$D = \frac{72}{9} = 8$ .

According to the rule of 72, the doubling time for this interest rate is 8 years.

Exact answer:

The exact answer is going to be found using the compound interest formula.

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

In which A is the amount of money, 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 t and t is the time the money is invested or borrowed for.

So, for this exercise, we have:

We want to find the doubling time, that is, the time in which the amount is double the initial amount, double the principal.

is double the initial amount, double the principal.

$A = 2P$

$r = 0.09$

The interest is compounded anually, so $n = 1$

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

$2P = P(1 + \frac{0.09}{1})^{t}$

$2 = (1.09)^{t}$

Now, we apply the following log propriety:

$\log_{a} a^{n} = n$

So:

$\log_{1.09}(1.09)^{t} = \log_{1.09} 2$

$t = 8.04$

The exact doubling time of this amount is 8.04 years.

4 0

4 years ago

(10 POINTS AND BRAINLIEST FOR BEST). Last month Ben spent $380 on food and $420 on personal items.

lions [1.4K]

4000 is his total monthly balance.

420 + 380 = 800

800/4000 = 0.20

0.20 = 20%

He spent 20% of his monthly income on food and personal items.

6 0

3 years ago

Karl uses 8 whole square tiles and 8 half square tiles to make a mosaic. What is the area of his mosaic?

trapecia [35]

Answer:

48

Step-by-step explanation:

8 squares=32

8 half squares=16

32+16=48

There are 4 sides to a 8 whole squares 8*4=32

There a 2 sides to 8 half squares 8*2=16

8 0

3 years ago

If this is wrong I WILL report you

MaRussiya [10]

The correct answer is #2: 6,2 9,3 12,4 because all of these answers equal 1/3

4 0

4 years ago

Georgia bought a packge of of 14 dollies to use in her valentines.She used 5/7 of the package to make her in valentines. How man

max2010maxim [7]

Answer: Georgia used 10 dollies and she has left 4 dollies .

Step-by-step explanation:

Given: Georgia bought a package of of 14 dollies to use in her valentines.

Therefore, the number of dollies in a package = 14

If she used $\frac{5}{7}$ of the package to make her in valentines.

The number of dollies she used = $\frac{5}{7}\times14=5\times2=10$

The number of dollies left = $14-10=4$

Hence, Georgia used 10 dollies and she has left 4 dollies .

5 0

3 years ago

brainliest answer points question in the photo!!