Please Help!
The number of cars sold weekly by a new automobile dealership grows according to a linear growth model. The first week the dealership sold five cars (P0=5
). The second week the dealership sold cars (P1=12
Pn = Pn−1+7
12-5=7
Pn=5+7n
If this trend continues, how many cars will be sold in the fourth week?
This was an incorrect answer
You would have sold 26 cars. 5+7(3)=26. Hope it helps future people.
If you're talking linear growth as a fixed rate of increase over time, you're increase would be 4 cars per week. You might assume a three-fold increase, but that wouldn't be linear. So 2 cars in week 1, 6 in week 2, 10 in week 3, and 14 in week 4. Add up all the cars sold (because you want to know how much he made in the first 4 weeks) and you get 32. 32 x $100 = $3,200.
Fair pay for a week (before taxes, though).
Why did the car dealership hire a clown? Because they needed someone to keep all the car sales from getting too serious! But don't worry, I'm here to help with your question.
According to the given linear growth model where Pn = Pn−1+7, we can find out how many cars will be sold in the fourth week.
Using the equation Pn = 5 + 7n, where n represents the number of weeks, we can substitute n with 4:
P4 = 5 + 7(4)
P4 = 5 + 28
P4 = 33
So, if the trend continues, the dealership will sell 33 cars in the fourth week. Keep that clown happy!
To find out how many cars will be sold in the fourth week if the trend continues, we can use the linear growth model equation:
Pn = Pn-1 + 7
The equation represents the number of cars sold in the nth week (Pn), which is equal to the number of cars sold in the previous week (Pn-1) plus 7 (since each week the dealership sells 7 more cars).
We are given that in the first week, the number of cars sold is P0 =5. Using the equation, we can calculate the number of cars sold in the second week (P1):
P1 = P0 + 7 = 5 + 7 = 12
Now, let's find out how many cars will be sold in the fourth week (P3):
P3 = P2 + 7
= (P1 + 7) + 7
= (12 + 7) + 7
= 19 + 7
= 26
Therefore, if the trend continues, the dealership will sell 26 cars in the fourth week.
You know that
Pn = 5+7n
so, replace n with 4, and you get
P4 = 5+7*4 = 33