Natasha Awada, Paul La Rondie, Laurie Buchanan and, Jill Stevens Solutions for Chapter: Representing Equivalent Quantities: Exponentials and Logarithms, Exercise 36: Exercise 9L

Mo bought a new car from a showroom. The value, $\$P$ of Mo's car is modelled by $P\left(t\right)=20000(0.9{)}^{kt}+1000$, where $t$ is the number of years since Mo bought the car. After three years, the car was valued at $\$16000$. Find $k$.

Mo bought a new car from a showroom. The value, $\$P$ of Mo's car is modelled by $P\left(t\right)=20000(0.9{)}^{kt}+1000$, where $t$ is the number of years since Mo bought the car. After three years, the car was valued at $\$16000$. Find $k$. Mo will sell his car when it is worth $\$5000$. Determine the number of years, after buying the car, that Mo sells it.

For their homework, a class of students was asked to memorize $100$ Spanish words. The average number of words remembered, $W$, is modelled by $W\left(t\right)=84-10\ln (t+1)$, where $t$ is the number of days that have passed since the homework was set. State the average number of words remembered on the day the homework was set.

For their homework, a class of students was asked to memorize $100$ Spanish words. The average number of words remembered, $W$, is modelled by $W\left(t\right)=84-10\ln (t+1)$, where $t$ is the number of days that have passed since the homework was set. Find the average number of words remembered ten days after the homework was set.

For their homework, a class of students was asked to memorize $100$ Spanish words. The average number of words remembered, $W$, is modelled by $W\left(t\right)=84-10\ln (t+1)$, where $t$ is the number of days that have passed since the homework was set. Find the number of days that pass before students will, on average, remember fewer than half the words.

The radioactive substance plutonium has a half-life of $25000$ years. A sample of $500 \mathrm{kg}$ of plutonium is put into storage. After $t$ years have passed, the amount of plutonium remaining in a sample, $A$, is modelled by:

$A\left(t\right)=A_0(0.5{)}^{\frac{t}{25000}}$

where $A_0$ is the initial amount of plutonium in the sample. If the sample is stored for $100$ years find, to the nearest $\mathrm{kg}$, find how much plutonium remains when the sample is taken out of storage.

The radioactive substance plutonium has a half-life of $25000$ years. A sample of $500 \mathrm{kg}$ of plutonium is put into storage. After $t$ years have passed, the amount of plutonium remaining in a sample, $A$, is modelled by:

$A\left(t\right)=A_0(0.5{)}^{\frac{t}{25000}}$

where $A_0$ is the initial amount of plutonium in the sample. Find, to the nearest year, how long the sample was stored if $100 \mathrm{kg}$ remained when the sample was taken out.

Solve the given equation:

$2^x=3{\mathrm{e}}^{4x}$