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Vladimir [108]
3 years ago
14

An initial of the $100 is now valuated at $150. The annual interest rate is 5%, compounded continuously. The equation 100e^0.05=

150 represents the situation, where t is the number of years the money has been invested. About how long has the money been invested. Use calculator to round to the nearest whole number.
Mathematics
2 answers:
Amiraneli [1.4K]3 years ago
7 0

Answer:

If you need answers to the whole assignment

Step-by-step explanation:

1. Consider 8^x-4 = 8^10

Because the (blank a) are equal , the (blank b) must also be equal.

Answer: Bases, Exponents

The solution to the equation is 14

2.What equation is equivalent to 9^(x-3)=729?

Answer 3^x - 3 = 3^6

Solve: 9x - 3 = 729

Answer: x = 6

3. To solve 5(2^x+4)=15, first divide each side by

Answer: 5

Solve 5(2^x+4) = 15. Round to the nearest thousandth.

Answer: -2.415

4. Which of the following is the solution of 5e^2x- 4 = 11?

Answer: x=In3/2

5. Select all of the potential solution(s) of the equation 2log5x = log54.

Answer: 2,-2

What is the solution to 2log5x = log54?

Answer: 2

6. Which equation is equivalent to log5x3 - logx2 = 2?

Answer: 10^log5^3/x^2=10^2

Solve: log5x3 - logx2 = 2

Answer: 20

7. What is the solution to ln (x2 - 16) = 0?

Answer: x=+-(17)

8. Solve: ln 2x + ln 2 = 0

Answer: ¼

Solve: e^ 2x+5 = 4

Answer: x=(In4) - 5/2

9. Consider the equation log(3x - 1) = log2(8). Explain why 3x - 1 is not equal to Describe the steps you would take to solve the equation, and state what 3x - 1 is equal to.

Answer: The bases are not the same, so you cannot set 3x - 1 equal to 8.You can evaluate the logarithm on the right side of the equation to get .You can use the definition of a logarithm to write 3x - 1 = 1000.

10. An initial investment of $100 is now valued at $150. The annual interest rate is 5%, compounded continuously. The equation 100e^0.05t = 150 represents the situation, where t is the number of years the money has been invested. About how long has the money been invested? Use your calculator and round to the nearest whole number.

Answer: 8

tangare [24]3 years ago
4 0

Answer:

8 years approximately

The problem (I'm assuming is):

Solve 100e^{0.05t}=150.

I put a t in the problem where I suspected it in went.

Step-by-step explanation:

100e^{0.05t}=150

Divide both sides by 100:

e^{0.05t}=\frac{150}{100}

e^{0.05t}=1.5

Rewrite in logarithm form.

\ln(1.5)=0.05t

Divide both sides by 0.05:

\frac{\ln(1.5)}{0.05}=t

Put left hand side into calculator:

8.109 \approx t

t \approx 8.109

So about 8 years if I wrote down the equation correctly.

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List the single-digit divisors of 2100.<br> I really need help
liberstina [14]

Answer:

  • 1, 2, 3, 4, 5, 6, 7

Step-by-step explanation:

<u>Prime factors of 2100 are:</u>

  • 2100 = 2*2*3*5*5*7

<u>The single-digit divisors are:</u>

  • 1, 2, 3, 2*2= 4, 5, 2*3= 6, 7

-----------------------------------------------------------------

<u>Another solution is you divide 2100 by all numbers 1 through 9 and list those divisible:</u>

  • 2100/1 = 2100, yes
  • 2100/2 = 1050, yes
  • 2100/3 = 700, yes
  • 2100/4 = 525, yes
  • 2100/5 = 420, yes
  • 2100/6 = 350, yes
  • 2100/7 = 300, yes
  • 2100/8 = 262.5, no
  • 2100/9 = 233.33, no

So all the numbers from 1 to 7

5 0
3 years ago
What is the area of this figure? ​
Delvig [45]

Answer:

33

Step-by-step explanation:

5 0
2 years ago
Workers have been down the street installing two blinking red lights in front of the fire station. The two lights are always tur
daser333 [38]

Answer:

After 88 seconds, they will blink together.

Step-by-step explanation:

Time after which the first light blinks = 8 seconds

Time after which the second light blinks = 22 seconds

Initially, both the lights blink together.

To find:

The time at which they will blink together again.

Solution:

Let us have a look at the time after which each light will blink.

First light will blink after:

8 s, 16 s, 24 s, 32 s, 40 s, 48 s, 56 s, 64 s, 72 s, 80 s, <em>88 s</em>, 96 s, 104 s, ......

Second light will blink after:

22 s, 44 s, 66 s, <em>88 s</em>, 110 s, .....

It can be seen that common time is 88 second, at which the both will blink together.

So, the answer is <em>88 s.</em>

<em></em>

This answer can also be computed by taking the LCM (Least Common Multiple) of both the numbers i.e. 8 and 22.

Using the factorization method:

8=\underline{2}\times 2\times 2

22=\underline{2}\times 11

Common is 2.

Therefore the LCM will be:

2\times 2\times2\times 11 = \bold{88}

So, the answer is <em>88 s.</em>

5 0
3 years ago
P + (-q) -3 when p= -6 and q=7
DochEvi [55]
Remember, -(-x)=x because the negatives cancel out

so
when p=-6 and q=7

p+(-q)-3
-6+(-7)-3
-6-7-3
-13-3
-16
5 0
3 years ago
-13 + 24-46-( - 20 ) =
Naddik [55]

Answer

-15

Step-by-step explanation:

-13 +24=11

11-46=-35

-35+20=-15

3 0
3 years ago
Read 2 more answers
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