7. i need with question in the attached picture!

The answer is approximately 3 years ⇒ answer B

Step-by-step explanation:

* Lets talk about the compound continuous interest  

- Compound continuous interest can be calculated using the formula:  

 A = P e^rt  

# A = the future value of the investment, including interest  

# P = the principal investment amount (the initial amount)

# r = the interest rate  

# t = the time the money is invested for  

- The formula gives you the future value of an investment,  

  which is compound continuous interest plus the

  principal.  

- If you want to calculate the compound interest only, you need  

 to deduct the principal from the result.  

- So, your formula is:

 Compounded interest only = Pe^(rt)  - P

* Now lets solve the problem

∵ P = $ 6000

∵ A = $ 8000

∵ r = 9/100 = 0.09

∵ t = ?  

∵ A = P e^(r t)

∴ 8000 = 6000 e^(0.09 × t) ⇒ divide both sides by 6000

∴ 4/3 = e^(0.09 × t) ⇒ insert ㏑ for both sides

∴ ㏑(4/3) = ㏑ e^(0.09 × t) ⇒ (㏑e = 1)

∴ ㏑(4/3) = 0.09 t ⇒ divide the both sides by 0.09

∴ t = [㏑(4/3)] ÷ 0.09 = 3.196467 ≅ 3 years