Exponential Model Word Problems Practice

1. Noah borrows $\$2000$ from his father and agrees to repay the loan and any interest determined by his father as soon as he has the money.

   The relationship between the amount of money, $A$, in dollars that Noah owes his father (including interest), and the elapsed time, $t$, in years, is modeled by the following equation.

   $A=2000e^{0.1t}$

   How long did it take Noah to pay off his loan if the amount he paid to his father was equal to $\$2450$?

   Give an exact answer expressed as a natural logarithm.

2. Katya is a ranger at a nature reserve in Siberia, Russia, where she studies the changes in the reserve's bear population over time.

   The relationship between the elapsed time $t$, in years, since the beginning of the study and the bear population $B(t)$, on the reserve is modeled by the following function.

   $B(t)=5000 \cdot 2^{-0.05t}$

   In how many years will the reserve's bear population be $2000$?

   Round your answer, if necessary, to the nearest hundredth.

3. Harper uploaded a funny video of her dog onto a website.

   The relationship between the elapsed time, $d$, in days, since the video was first uploaded, and the total number of views, $V(d)$, that the video received is modeled by the following function.

   $V(d)=4^{{1.25d}}$

   How many views will the video receive after $6$ days?

   Round your answer, if necessary, to the nearest hundredth.

4. A huge ice glacier in the Himalayas initially covered an area of $45$ square kilometers. Because of changing weather patterns, this glacier begins to melt, and the area it covers begins to decrease exponentially.

   The relationship between $A$, the area of the glacier in square kilometers, and $t$, the number of years the glacier has been melting, is modeled by the following equation.

   $A=45e^{-0.05t}$

   How many years will it take for the area of the glacier to decrease to $15$ square kilometers?

   Give an exact answer expressed as a natural logarithm.
   

Source: Khan Academy, https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:logs/x2ec2f6f830c9fb89:exp-models/e/exponential-models-word-problems
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