Rose Harrison, Clara Huizink, Aidan Sproat Clements and, Marlene Torres Skoumal Solutions for Exercise 16: Mixed practice

Find the value of $x$ to the nearest hundredth:

$\log 650=x$.

Find the value of $x$ to the nearest hundredth:

$\ln 5=x$.

The table below shows the average movie ticket price in Canada from $1990\text{ to }1994$.

$\begin{array}{|cc|}\hline \text{ Year }& \begin{array}{c}\text{ Price of a }\\ \text{ movie ticket (\$) }\end{array}\\ 1990& 4.00\\ 1991& 4.22\\ 1992& 4.45\\ 1993& 4.70\\ 1994& 4.96\\ \hline\end{array}$

Find the exponential model for the average movie ticket price as a function of $t$, the number of years since $1990$.

The table below shows the average movie ticket price in Canada from $1990\text{ to }1994$.

$\begin{array}{|cc|}\hline \text{ Year }& \begin{array}{c}\text{ Price of a }\\ \text{ movie ticket (\$) }\end{array}\\ 1990& 4.00\\ 1991& 4.22\\ 1992& 4.45\\ 1993& 4.70\\ 1994& 4.96\\ \hline\end{array}$

Calculate the average price of a movie ticket in the year $2016$ . [Use $e^{1.37800}=3.96695977$]]

The table below shows the average movie ticket price in Canada from $1990\text{ to }1994$.

$\begin{array}{|cc|}\hline \text{ Year }& \begin{array}{c}\text{ Price of a }\\ \text{ movie ticket (\$) }\end{array}\\ 1990& 4.00\\ 1991& 4.22\\ 1992& 4.45\\ 1993& 4.70\\ 1994& 4.96\\ \hline\end{array}$

Find when the average price will reach $\$20$ . [Use $e^{1.37800}=3.96695977$]

A kettle of water is heated and then allowed to cool. The temperature can be modelled by the exponential equation $T=100e^{-0.2t}$, where $T$ is the temperature $\left(\text{ in }°C\right)$ and $t$ is the time in minutes. Find the initial temperature.

A kettle of water is heated and then allowed to cool. The temperature can be modelled by the exponential equation $T=100e^{-0.2t}$, where $T$ is the temperature $\left(\text{ in }°C\right)$ and $t$ is the time in minutes. Determine the temperature after $3$ minutes.  [Use $e^{-0.6}=0.548811636$]

A kettle of water is heated and then allowed to cool. The temperature can be modelled by the exponential equation $T=100e^{-0.2t}$, where $T$ is the temperature $\left(\text{ in }°C\right)$ and $t$ is the time in minutes. Elizabeth can drink the water when the temperature is $40°C$. Find how long she must leave it to cool.  [Use $\ln 0.4=-0.916290732$]