For the function:  $y=3^x+4$

(i) Sketch the graph and mark the asymptote as a dashed line(if the asymptote is not the x-axis).

(ii) Label the coordinates of the y-intercept on your graph.

(iii) Write down the equation of asymptote.

(iv) Label the coordinates of one additional point on the curve(other than the y-intercept).

(v) State the domain and range.

 

 

 

For the function:  $y=2^{-x}-3$

(i) Sketch the graph and mark the asymptote as a dashed line(if the asymptote is not the x-axis).

(ii) Label the coordinates of the y-intercept on your graph.

(iii) Write down the equation of asymptote.

(iv) Label the coordinates of one additional point on the curve(other than the y-intercept).

(v) State the domain and range.

For the function :  $y=2-2^x$

(i) Sketch the graph and mark the asymptote as a dashed line(if the asymptote is not the x-axis).

(ii) Label the coordinates of the y-intercept on your graph.

(iii) Write down the equation of asymptote.

(iv) Label the coordinates of one additional point on the curve(other than the y-intercept).

(v) State the domain and range.

Teacher Tom makes a cup of coffee and leaves it on his table.

Its temperature $\left(H^{°}C\right)$ is modelled by the function $H=\left(65\right)2^{-\frac{t}{2}}+25,$ where $t$ is the time in minutes after Tom makes the coffee.

State the initial temperature of the coffee.

Teacher Tom makes a cup of coffee and leaves it on his table.

Its temperature $\left(H^{°}C\right)$ is modelled by the function $H=\left(65\right)2^{-\frac{t}{2}}+25,$ where $t$ is the tie in minutes after Tom makes the coffee.

Find the temperature of the coffee after $3$ minutes.

Teacher Tom makes a cup of coffee and leaves it on his table.

Its temperature $\left(H^{°}C\right)$ is modelled by the function $H=\left(65\right)2^{-\frac{t}{2}}+25,$ where $t$ is the tie in minutes after Tom makes the coffee.

Tom likes to drink his coffee when it is ${40}^{°}C$ or cooler. Find, to the nearest minute, how long he should he wait to drink his coffee. [Use logarithmic table if required ]

Teacher Tom makes a cup of coffee and leaves it on his table.

Its temperature $\left(H^{°}C\right)$ is modelled by the function $H=\left(65\right)2^{-\frac{t}{2}}+25,$ where $t$ is the tie in minutes after Tom makes the coffee.

Determine the temperature of the room where Tom set down his coffee.

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.

Find the value of the car when it was new.

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.

Determine the value of the car when it is $3$ years old.