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# 18 I can solve problems involving e and In.
0.0.15t


3. The expression 1 e models the balance, in thousands of dollars, where t represents
time in years after the account was opened.

a. What does the 0.015 represent in this context?

b. Write an expression and for the number of years after which there will be $8,000 in the
account and simplify.

4. Explain why In 16 is greater than 2 but less than 3.

Answer :

The expression is assumed here as it's unclear looking

If it's P=(P_o)ln0.015t then the below solution of Part B is correct else they may vary.

#a

  • 0.015 represents rate of change with respect to t.

#b

As per our assumed equation

It's.

  • 8000=(P_o)ln0.015^t

Simplify

  • tln0.015=8000/P_o

Initial amount of account is not given so you have to solve the above equation after putting known P_o

#3

  • ln16
  • ln4²
  • 2ln4
  • 2(1.38)
  • 2.76(Approx)

Hence it's less than 3 and greater than 2

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