Question

A company deposits $25,000 in a bank account that earns interest. The value of the account can be represented as 25,000e^0.0198t, where t represents time, in years.
The time, t, in years that it will take for the account to have a value of $30,000 can be modeled as t=ln(k)/0.0198. What is the value of k?

Answer 1

Answer:

  k = 1.2

Step-by-step explanation:

Solving for t when the account value is 30,000, we have ...

  30,000 = 25,000e^(0.0198t)

  30,000/25,000 = 1.2 = e^(0.0198t)

  ln(1.2) = 0.0198t

  t = ln(1.2)/0.0198

Matching this with the form ...

  t = ln(k)/0.0198

we see that k = 1.2.

_____

k is the multiplier of account value in time period t.