An initial investment of $100 is now valued at $150. the annual interest rate is 5%, compounded continuously. the equation 100e0.05t = 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. years

 

Step-by-step explanation:

we know that

The formula to calculate continuously compounded interest is equal to

 

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest in decimal  

t is Number of Time Periods  

e is the mathematical constant number

we have  

 

substitute in the formula above  

 

 

Applying ln both sides

 

 

 

 

If you need all the answers for that 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.

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

x = 6

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

5

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

-2.415

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

x=In3/2

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

2,-2

What is the solution to 2log5x = log54?

2

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

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

Solve: log5x3 - logx2 = 2

20

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

x=+-(17)

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

¼

Solve: e^ 2x+5 = 4

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.

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.

8

8 years

Step-by-step explanation:

An initial investment of $100 is now valued at $150. The annual interest rate is 5%, compounded continuously. The equation represents the situation, where t is the number of years the money has been invested.

To find out how long has the money invested we need to find out 't'

, solve for t

divide both sides by 100

Now to remove 'e' we take ln on both sides

the value of

Now divide by 0.05 on both sides

t = 8.10930

The money is invested for 8 years

8

Step-by-step explanation:

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