Question

Plz help will give wut i got (as in points)

Temperature in the desert can be modeled by the function C(t), where t represents hours after midnight (0 ≤ t ≤ 24), and C is the temperature measured in degrees Celsius. Examine what happens to the graph when you transform the function to degrees Fahrenheit.
Circle the desert you picked:

Sahara Desert Patagonian Desert Death Valley California

Exploring Degrees Celsius
1. Fill out the following chart to find the temperatures for t = 12 (noon) and t = 24 (midnight). (2 points: 1 point for each row)
t C(t) = –0.30(t – 12)2 + 40
0
12




24




2. Plot the three points from the chart onto the graph below. Use the plotted points to sketch the graph of C(t) = –0.30(t – 12)2 + 40. (3 points: 2 points for correct coordinates, 1 point for correct shape)

Convert the Function to Degrees Fahrenheit:
3. Suppose you want to represent the desert temperature in degrees Fahrenheit instead. How would you transform the function C(t) to make the new function, F(t)? (2 points: 1 point for each transformation)
Note: The conversion rule for Celsius to Fahrenheit is .






4. Take your values from the previous chart (in question 2) and convert them from Celsius to Fahrenheit. Follow the example below, and use the conversion rule to fill out the chart for degrees Fahrenheit when t = 12 and t = 24. (2 points: 1 point for each row)
t
0
12






24






5. Use the conversion formula to write the equation for the new function, F(t).
(4 points: 2 points for setting up the equation, 2 points for the answer)
Hint: Substitute the equation for C(t) into .












6. Plot the points from the Fahrenheit chart in question 4 onto the graph below. Use the plotted points to sketch out the graph of F(t). (3 points: 2 points for correct coordinates, 1 point for correct shape)

7. Compare the graph in question 6 (F(t)) with the graph in question 2 (C(t)). What changes were made to the graph of C(t) to transform it to F(t)? (1 point)

Answer 1

problems 4,5,6,7 (make sure you add °C to the answers given in step one above) *note, these answers given in both answers could be used for any of the deserts chosen, they all have the same formula given.

Explanation:

4) box 12

(12,40)

f(12)= 9/5 (40)+ 32

f(12)= 72 +32

f(12)= 104 ° F

box 24

(24, -3.2)

f(24)= 9/5 (-3.2) +32

f(24) = -5.76 +32

f(24)= 26.24 °F

5.

substitute the given C(t) equation into the conversion formula

F(t)= 9/5C(t)+32.

We know from the information given that C(t)=−0.30(t−12)^2 +32

to solve:

F(t)= 9/5[−0.30(t−12)^2+40]+32

F(t)=1.8(−0.3t^2+7.2t−3.2)+32

F(t)=−0.54t^2+12.96t−5.76+32

F(t)=−0.54t^2+12.96t+26.24

6.

on the graph plot the three points (0,-0.32), (12,104), (24,-0.32)

It draw the lines to connect the bottom two points to 12, 104, It should look like upside down V but curved softer like the graph in answer number 2.

7. The changes made to the graph of C(t) to transform it to F(t) was changing the noon temperature (plot point) from 40° C to 104° F. It increased the steepness of the graph.