| {{ 'ml-lesson-number-slides' | message : article.intro.bblockCount }} |
| {{ 'ml-lesson-number-exercises' | message : article.intro.exerciseCount }} |
| {{ 'ml-lesson-time-estimation' | message }} |
Here are a few recommended readings before getting started with this lesson.
Dominika, a budding citizen scientist, is curious about the changes in temperature where she lives in Phoenix, Arizona. Since she walks to school everyday, the temperature affects her walk. Dominika decides to measure the temperature at three different times on the same day. Here are the measurements she recorded.
Time | Temperature |
---|---|
16:00 | 94∘F |
19:00 | 88∘F |
21:00 | 78∘F |
When was the temperature decreasing the fastest: between 16:00 and 19:00 or between 19:00 and 21:00?
Calculate the change in time and temperature. Use the formula for the rate of change.
Time Interval | Δt | ΔT |
---|---|---|
16:00−19:00 | 3 hours | -6∘F∣∣∣∣94−88= |
19:00−21:00 | 2 hours | -10∘F∣∣∣∣88−78= |
Now, substitute the obtained values of ΔT and Δt into the formula to find the rate of change of each time interval.
Time Interval | Δt | ΔT | Rate of Change |
---|---|---|---|
16:00−19:00 | 3 hours | -6∘F | 3-6=-2∘F per hour |
19:00−21:00 | 2 hours | -10∘F | 2-10=-5∘F per hour |
As can be seen, the temperature decreased at an average rate of 2∘F in the first time interval and 5∘F in the second time interval. Therefore, the temperature decreased the fastest between 19:00 and 21:00.
Along the walk to school, Dominika passes her father's 24-hour cafe. Running the cafe requires close attention to customer behavior. Her father notices that it is typical to serve 1 customer each night from 2:00 AM till 4:00 AM. Then, starting from 6:00 AM, the cafe slowly begins to fill with regulars.
Let P represent the number of people in the cafe and t represent the time in hours since midnight.
Equation | Meaning |
---|---|
f(12)=20 | At 12:00 PM, there are 20 customers in the cafe. |
f(14)−f(12)=20 | The difference between the number of customers at 12:00 PM and the number of customers at 2:00 PM is 20 people. |
2f(14)−f(12)=20 | The average change of the number of customers per hour between 12:00 PM and 2:00 PM is 20 people. |
P=f(12)+20 | The number of people at the cafe equals the number of customers at 12:00 PM plus 20 more customers. |
The second equation can be rephrased as the number of customers at 2:00 PM increased by 20 since 12:00 PM, which coincides with what Mr. Beckett observed. Therefore, this equation best represents the described situation.
While walking to school, Zosia was thinking about a story her auntie just told her. In the windy city crazy winds, flurries of snow, and a max capacity of 61500 cheering fans have been a part of the legacy of Soldier Field, where the Chicago Bears have played on the gridiron each Sunday for decades. The average cost of ticket to a game was $45 at some point in time.
Zosia's auntie went to a game against there rivals, only to hear that the owner was thinking of selling the team. If only they could make more money from ticket sales! The amount of money earned from the game her auntie attended is a function of the number of people n who attended it.
Help Dominika find the needed functions so that she can finish her app.
x=0, f(x)=-459.67
Zero Property of Multiplication
Identity Property of Addition
Rearrange equation
x=310.15, f(x)=98.6
LHS+459.67=RHS+459.67
Rearrange equation
LHS/310.15=RHS/310.15
LHS+459.67=RHS+459.67
Rewrite 1.8 as 1018
ba=b/2a/2
LHS⋅95=RHS⋅95
Rearrange equation
Dominika's father, the chef, knows that his daughter and her friends love to stop by his cafe along their walk home from school on Fridays. He is eager to expand his menu and add flor de calabaza quesadillas because it is his daughter's favorite!
Her father has calculated that there would be a weekly fixed cost of $75 for adding a new dish plus an additional $0.7 for the ingredients per quesadilla. The total cost C for preparing x quesadillas can be represented by a linear function.Number of Quesadillas Sold | 10 | 25 | 50 | 75 | 100 | 200 |
---|---|---|---|---|---|---|
Total Cost | ||||||
Cost per Quesadilla | ||||||
Sales Price per Quesadilla |
Price of One Quesadilla: $4
Number of Quesadillas Sold | 10 | 25 | 50 | 75 | 100 | 200 |
---|---|---|---|---|---|---|
Total Cost | $82 | $92.50 | $110 | $127.50 | $145 | $215 |
Cost per Quesadilla | $8.20 | $3.70 | $2.20 | $1.70 | $1.45 | $1.08 |
Sales Price per Quesadilla | $8.50 | $4.00 | $2.50 | $2.00 | $1.75 | $1.38 |
x=25
Multiply
Add terms
Number of Quesadillas Sold | 10 | 25 | 50 | 75 | 100 | 200 |
---|---|---|---|---|---|---|
Total Cost | $82 | $92.50 | $110 | $127.50 | $145 | $215 |
Cost per Quesadilla | $8.20 | $3.70 | $2.20 | $1.70 | $1.45 | $1.08 |
Sales Price per Quesadilla | $8.50 | $4.00 | $2.50 | $2.00 | $1.75 | $1.38 |