Decide whether each situation is best described by a linear or quadratic function.
MTV Royalties
MTV paid a songwriter $1000 to use the recording on their show. After that, the songwriter gets a check for $26 in performance royalties for their songwriting every time the episode airs.
1 Do royalties increase or decrease over time?
2 When the songwriter agrees to let MTV use the recording on their show (x=0), how much money do they earn?
3 How many dollars will they have after…
| (first airing) x = 1 |
(second airing) x = 2 |
x = 3 | x = 4 |
|---|---|---|---|
|
4 What is the form of this function? ☐ linear ☐quadratic
Tuition Savings Account
A family managed to save $18,000 by the time their child started studying to be an electrician at the community college, where tuition and fees cost $2200 per semester.
5 When the child starts college (x=0), how many dollars are in the account?
6 Will the money in the account increase or decrease while they’re in college?
7 How many dollars will be in the account after…
| (paying for semester 1) x=1 |
x= 2 | x = 3 | x = 4 |
|---|---|---|---|
|
8 What is the form of this function? ☐ linear ☐quadratic
Stopping Time
In a certain car, from the time a driver steps on the breaks, the vehicle decelerates at a rate of 10 meters per second. We can calculate the time it takes to stop the car, by squaring the speed it’s driving in meters per second and dividing by 20.
9 How long does it take to stop the car when it’s driving at 0 km/h (x=0)?
10 Does stop time increase or decrease as speed increases?
11 What is stopping time when it’s driving at a speed of…
First, we’ll need to convert driving times from kilometers/hour to meters/second.
$$\displaystyle \frac{\text{10 kilometers}}{1 hour} \times \frac{\text{1 hour}}{\text{3600 seconds}} \times \frac{\text{1000 meters}}{\text{1 kilometer}} = \frac{10\require{enclose}\enclose{horizontalstrike}{\text{kilometers}} \times 1\require{enclose}\enclose{horizontalstrike}{\text{hour}} \times \text{1000 meters}} {1\require{enclose} \enclose{horizontalstrike}{\text{hour}} \times \text{3600 seconds} \times 1\require{enclose}\enclose{horizontalstrike}{\text{kilometer}}} = \frac{10000}{3600} \text{meters per second} = 2.778 \text{m/s}$$
| (10 km/h = 2.778 m/s) x=10 |
(20 km/h = 5.555 m/s) x=20 |
x=30 | x =40 |
|---|---|---|---|
|
12 What is the form of this function? ☐linear ☐ quadratic
These materials were developed partly through support of the National Science Foundation, (awards 1042210, 1535276, 1648684, 1738598, 2031479, and 1501927). 
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