Number of new cars purchased in a city can be modeled by the equation

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In summary, the first conversation is asking for help with two problems. The first is about finding the year in which the number of new cars will reach 38,000, given an equation for modeling car purchases. The second problem involves determining the model for the total number of grapes sold from 1992-1996, based on equations for the average number of green and red grapes sold during those years. Hints are given for both problems to guide the person towards solving them.
  • #1
gigi9
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Help ASAP please!

Can someone please show me how to do the 2 problems below? I really don't know how...Thanks
1)The number of new cars purchased in a city can be modeled by the equation C=22t^2+17tt+9933, where C is the number of new cars and t=0 corresponds to the number of new cars purchased in 1976. In what year will the number of new cars reach 38,000?

2)During the years 1992-1996, the average number of green grapes, G, sold by a large farmer's market can be modeled by
G= -11t^2+2.02t+41.09. The average number of red grapes, R, sold by the farmer's market can be modeled by R= .004t^2-.688t+79.06. Determine the model representing the number of grapes, N, sold from 1992-1996.
 
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  • #2
Here are some hints for you.

1)The number of new cars purchased in a city can be modeled by the equation C=22t^2+17t+9933, where C is the number of new cars and t=0 corresponds to the number of new cars purchased in 1976. In what year will the number of new cars reach 38,000?
We know C corresponds to the number of new cars purchased. You are given an equation showing the relation between C, number of cars purchased and t, where t=0 in 1976.
Can you use 38 000, which is the number of new cars sold in a particular year, to find out t? (Hint: you need to solve a quadratic equation)
After t is found, how can you relate t to the year 38000 cars are sold? (Hint, t=0 represents year 1976, how about t=1, t=2 and so on?)

2)During the years 1992-1996, the average number of green grapes, G, sold by a large farmer's market can be modeled by
G= -11t^2+2.02t+41.09. The average number of red grapes, R, sold by the farmer's market can be modeled by R= .004t^2-.688t+79.06. Determine the model representing the number of grapes, N, sold from 1992-1996.

You can use the way question 1 was asked as a reference.
Take t=1 represent year 1992.

In 1992, the average number of green grapes sold:
G1992= -11t^2+2.02t+41.09
the average number of red grapes sold:
R1992= .004t^2-.688t+79.06
total number of grapes sold in 1992 = G1992+R1992

In 1993, the average number of green grapes sold,
G1993 = -11(t+1)^2+2.02(t+1)+41.09
The average number of red grapes sold:
R1993= .004(t+1)^2-.688(t+1)+79.06.
Total number of grapes sold in 1993 = R1993+G1993

Can you continue from here?
 
  • #3
And we have a homework help forum specifically for, well, homework help.
 

1. What factors are included in the equation for modeling the number of new cars purchased in a city?

The equation for modeling the number of new cars purchased in a city typically includes variables such as population size, average income, and current market trends. These factors can vary depending on the specific model being used.

2. How accurate is the model for predicting the number of new cars purchased in a city?

The accuracy of the model for predicting the number of new cars purchased in a city can vary. It is important to regularly update the model with current data and adjust for any changes in the market or population to improve accuracy.

3. Can the equation be used for any city or is it specific to a certain location?

The equation for modeling the number of new cars purchased in a city can be used for any city, but it may need to be adjusted for certain factors such as regional income differences or cultural preferences for certain types of cars.

4. How does the equation account for changes in technology and consumer preferences?

The equation may need to be updated or modified over time to account for changes in technology and consumer preferences, as these factors can greatly impact the number of new cars purchased in a city. Regularly collecting and analyzing data can help identify any necessary adjustments.

5. Is there a way to improve the accuracy of the model?

Yes, there are several ways to improve the accuracy of the model for predicting the number of new cars purchased in a city. Some suggestions include using more data points, including additional variables, and regularly updating the model with current data.

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