Question

question one spring day, evan noted the time of day and the temperature, in degrees fahrenheit. his findings are as follows: at 6 a.m., the temperature was 58° f. for the next 3 hours, the temperature rose 1° per hour. for the next 4 hours, it rose 2° per hour. the temperature then stayed steady until 6 p.m. for the next 3 hours, the temperature dropped 2° per hour. the temperature then dropped steadily until the temperature was 62° at midnight. on the set of axes below, graph evan’s data.

Explanation:

Step1: Calculate temp at 9 a.m.

Initial temp at 6 a.m.: $58^\circ\text{F}$. Rise $1^\circ$/hr for 3 hrs.
$58 + (1 \times 3) = 61^\circ\text{F}$

Step2: Calculate temp at 1 p.m.

Temp at 9 a.m.: $61^\circ\text{F}$. Rise $2^\circ$/hr for 4 hrs.
$61 + (2 \times 4) = 69^\circ\text{F}$

Step3: Note temp at 6 p.m.

Temp stays steady until 6 p.m.: $69^\circ\text{F}$

Step4: Calculate temp at 9 p.m.

Temp at 6 p.m.: $69^\circ\text{F}$. Drop $2^\circ$/hr for 3 hrs.
$69 - (2 \times 3) = 63^\circ\text{F}$

Step5: Confirm midnight temp

Given temp at midnight: $62^\circ\text{F}$. Rate from 9 p.m. to midnight: $\frac{63-62}{3} = \frac{1}{3}^\circ\text{F}$ per hour drop.

Answer:

Key temperature-time points for graphing:

• 6 a.m.: $58^\circ\text{F}$
• 9 a.m.: $61^\circ\text{F}$
• 1 p.m.: $69^\circ\text{F}$
• 6 p.m.: $69^\circ\text{F}$
• 9 p.m.: $63^\circ\text{F}$
• Midnight: $62^\circ\text{F}$

To graph: Plot these points, then draw straight line segments between consecutive points to show steady rise, steady temperature, and steady drop.