Answer:
8 years approximately
The problem (I'm assuming is):
Solve [tex]100e^{0.05t}=150[/tex].
I put a t in the problem where I suspected it in went.
Step-by-step explanation:
[tex]100e^{0.05t}=150[/tex]
Divide both sides by 100:
[tex]e^{0.05t}=\frac{150}{100}[/tex]
[tex]e^{0.05t}=1.5[/tex]
Rewrite in logarithm form.
[tex]\ln(1.5)=0.05t[/tex]
Divide both sides by 0.05:
[tex]\frac{\ln(1.5)}{0.05}=t[/tex]
Put left hand side into calculator:
[tex]8.109 \approx t[/tex]
[tex]t \approx 8.109[/tex]
So about 8 years if I wrote down the equation correctly.
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
