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zhuklara [117]
3 years ago
12

Need help with #11. The answer is about 13.86 years but show work please.

Mathematics
1 answer:
tangare [24]3 years ago
6 0

Answer:

13.86

Step-by-step explanation:

formula for cont. compounding interest is

Amount = Principal * e^rt

in this case the principal is 5000, and the amount is 10000 (double). the rate is 5% or 0.05. and t is what we are solving for.

sub in to get:

10000 = 5000e^0.05t

2 = e^0.05t

now convert to log form.

ln 2 = 0.05t

ln 2 / 0.05 = t

punch that into your calculator and you get 13.86 years

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9514 1404 393

Answer:

  • $3000 at 8%
  • $4000 at 6%

Step-by-step explanation:

Let x represent the amount invested at 8%. Then the total interest earned is ...

  0.06(7000 -x) +0.08x = 480

  420 +0.02x = 480 . . . . . . . . . eliminate parentheses

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$3000 was invested at 8%; $4000 was invested at 6%.

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PLEASE HELP: Simplify the expression. Write your answer as a power. 5^2⋅5^9/5
antoniya [11.8K]

Answer:

9.765625×10^6

Step-by-step explanation:

Simplify the following:

5^2×5^9/5

Hint: | Express 5^2×5^9/5 as a single fraction.

5^2×5^9/5 = (5^2×5^9)/5:

(5^2×5^9)/5

Hint: | For all exponents, a^n/a^m = a^(n - m). Apply this to (5^2×5^9)/5.

Combine powers. (5^2×5^9)/5 = 5^(9 + 2 - 1):

5^(9 + 2 - 1)

Hint: | Evaluate 9 + 2.

9 + 2 = 11:

5^(11 - 1)

Hint: | Subtract 1 from 11.

| 1 | 1

- | | 1

| 1 | 0:

5^10

Hint: | Compute 5^10 by repeated squaring. For example a^7 = a a^6 = a (a^3)^2 = a (a a^2)^2.

5^10 = (5^5)^2 = (5×5^4)^2 = (5 (5^2)^2)^2:

(5 (5^2)^2)^2

Hint: | Evaluate 5^2.

5^2 = 25:

(5×25^2)^2

Hint: | Evaluate 25^2.

| 2 | 5

× | 2 | 5

1 | 2 | 5

5 | 0 | 0

6 | 2 | 5:

(5×625)^2

Hint: | Multiply 5 and 625 together.

5×625 = 3125:

3125^2

Hint: | Evaluate 3125^2.

| | | 3 | 1 | 2 | 5

× | | | 3 | 1 | 2 | 5

| | 1 | 5 | 6 | 2 | 5

| | 6 | 2 | 5 | 0 | 0

| 3 | 1 | 2 | 5 | 0 | 0

9 | 3 | 7 | 5 | 0 | 0 | 0

9 | 7 | 6 | 5 | 6 | 2 | 5:

Answer: | 9765625 = 9.765625×10^6

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2 years ago
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