Question

The population of Nevada, P(t), in millions of people, is a function of t, the number of years since 2010. Explain the meaning of the statement P(8) = 3. Use units and everyday language. (1 point)
2. Find the slope-intercept form of the equation of the line through the points (8, 25) and (-2, -13). (2 points)
3. At 8am, Charles leaves his house in Spartanburg, SC and drives at an average speed of 65 miles per hour toward Orlando, FL. At 11:45am, he stops for lunch in Savannah, GA, which is 276.25 miles from Orlando. a. Find a linear formula that represents Charles’ distance, D, in miles from Orlando as a function of t, time in hours since 8am. (2 points)
b. Find and interpret the horizontal intercept. Remember to write your intercept as a point! (2 points)
c. Find and interpret the vertical intercept. Remember to write your intercept as a point! (2 points)
1
2
4. The temperature in ◦F of freshly prepared soup is given by T(t) = 72 + 118e−0.018t, where t represents time in minutes since 6pm when the soup was removed from the stove. a. Determine the value of T(30) and interpret your answer in everyday language. (2 points)
b. Find and interpret the vertical intercept. Remember to write your intercept as a point! (2 points)
5. Decide whether the following function is linear. Explain how you know without finding the equation of the line.
x 9 12 16 23 34 f(x) 26.6 36.2 49 74.9 110.1
6. Attendance at a local fair can be modeled by A(t) = −30t2 + 309t + 20 people, where t represents the number of hours since 10am. a. Find the average rate of change of the attendance from t = 3 to t = 8. Give units. (2 points)
b. Interpret your answer from (a) in everyday language.

Answer 1

1.   means 3 millions of people in Nevada in the year 2010 + 8 = 2018.

2. slope intercept equation of a line is   , m is the slope and c is the intercept.  

two points are given (8,25) and (-2,-13) , slope ,   

on substituting we get   

to find intercept c substitute (8,25) in line equation, that is    which give   

therefore we can write line equation as on multiplying both side by 5 , we get

  

3. a. since 8 am distance can be calculated as product of average speed and time taken. so we can write for 8 am to 11:45 am. after 11:45 there come initial distance of   

so after 11:45 am equation becomes

b. for time 8 - 11:45 am horizontal intercept is 0 or origin

for time after 11:45 am horizontal intercept is ,     

so here in practical t cannot be negative still in theory we can extend line to this intercept  

c. for time 8 - 11:45 am vertical or y intercept is 0 or origin

for time after 11:45 am vertical intercept is when so on substituting we get     

which gives vertical intercept as 243.75 or the point   

4. a. the temperature in is given by the equation    to evaluate    substitute t=30 in the equation so we get    which gives    so we can say that at time 6:30 pm when the freshly prepared soup was removed from the stove it shows a temperature of  

b. the vertical or y intercept is when so       so it is the temperature when the time is 6 pm when the soup was removed from the stove. so its the point   

5. On evaluating the slope of the function or line it is found that its slope changes which means the points do NOT lie on same line so it is NOT a linear function and slope is given by

6.a. given the average rate of change from t=3 to t=8 is given by   

which gives   as average rate of change

b. which means that after 10 am the attendance is having a negative rate of change which means its slope is negative so as time progresses A(t) or attendance decreases