Natasha Awada, Paul La Rondie, Laurie Buchanan and, Jill Stevens Solutions for Chapter: Representing Equivalent Quantities: Exponentials and Logarithms, Exercise 15: Exercise 9D

The value, $y$, of a car, in thousands of dollars, is modelled by the function $y=30{\left(0.9\right)}^x$, where $x$ is the number of years since the car was manufactured.

Use your GDC to estimate when the value of the car will be half of its original value.

The population $\left(P\right)$ of squirrels in a park is modelled by the function $P=40{\left(1.5\right)}^t$, where $t$ is the number of years that have elapsed since recording the squirrel population began.

State how many squirrels there were initially.

The population $\left(P\right)$ of squirrels in a park is modelled by the function $P=40{\left(1.5\right)}^t$, where $t$ is the number of years that have elapsed since recording the squirrel population began.

Estimate the population of squirrels in the park after two years.

The population $\left(P\right)$ of squirrels in a park is modelled by the function $P=40{\left(1.5\right)}^t$, where $t$ is the number of years that have elapsed since recording the squirrel population began.

By plotting a graph on your GDC, find how long will it take the population of squirrels to reach $200$.

The rate of decay of the radioactive substance carbon$-14$ can be modelled by the equation $A=A_o{\left(2\right)}^{\frac{t}{5730}}$, where $A$ is the mass of carbon$-14$ at the time $t$(measured in years) and $A_o$ is the initial mass.

If you start with $100$ mg of carbon$-14$, find how much will remain after $1000$ years.

The rate of decay of the radioactive substance carbon$-14$ can be modelled by the equation $A=A_o{\left(2\right)}^{\frac{t}{5730}}$, where $A$ is the mass of carbon$-14$ at the time $t$(measured in years) and $A_o$ is the initial mass.

Use technology to sketch the graph of the model with the time on the horizontal axis with $0\le t\le 8000$ and $0\le A\le 100$. Graph appropriate lines to approximate how many years(to the nearest year) until the mass is $75$ grams.

The rate of decay of the radioactive substance carbon$-14$ can be modelled by the equation $A=A_o{\left(2\right)}^{\frac{t}{5730}}$, where $A$ is the mass of carbon$-14$ at the time $t$(measured in years) and $A_o$ is the initial mass.

Use technology to sketch the graph of the model with the time on the horizontal axis with $0\le t\le 8000$ and $0\le A\le 100$. Graph appropriate lines to approximate how many years(to the nearest year) until the mass is halved.

The rate of decay of the radioactive substance carbon$-14$ can be modelled by the equation $A=A_o{\left(2\right)}^{\frac{t}{5730}}$, where $A$ is the mass of carbon$-14$ at the time $t$(measured in years) and $A_o$ is the initial mass.

Find the mass of carbon$-14$ after $1000$ years.