Question

Brian opened a bank account that compounded continuously. The amount, y, in Brian's account can be modeled by this equation.

y=nekt
Where n is the initial amount deposited,
t is the time in years, and
k is the growth constant.
Brian deposited $500 initially and did not make any more deposits or withdrawals. After 8 years, Brian's account has a balance of $625.
What is the value of k?
O A k =
In(.8)
8
O c. k=
In(500)
5000
O B. k=
In(625)
4000
O D. k=
In(1.25)
8

Answer 1

9514 1404 393

Answer:

D. k = In(1.25)/8

Explanation:

Solve the equation for k. Maybe you want to put the numbers in first.

`y=n\cdot e^(kt)\\\\625=500e^(8k)\qquad\text{use the given values}\\\\1.25=e^(8k)\qquad\text{divide by 500}\\\\ln((1.25))=8k\qquad\text{take the natural log}\\\\\boxed{k=(\ln(1.25))/(8)}\qquad\text{divide by 8}`

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That's about 2.7893%