Answer:
Car: 18.4% Other: 4.9%
Step-by-step explanation:
Glenn family yearly total expenses are
Other expenses are $7,000.
The payments for the new car are: $375.00 per month and the insurance for the new car $85.00 per month, in total, $460 per month. Yearly expenses for car are
Now, the expenses for the following two categories are
Car - $5,520
Other - $7,000 - $5,520 = $1,480
Percentage:
Car:
Other
Answer: first choice, exponential, because there is a relatively consistent multiplicative rate of change.
Explanation:
1) I have attached the figure with the data table that represents the temperature of a cup of coffee over time.
These are the data:
Time (min) ------ Temperature (°F)
0 ----------------------- 200
10 ---------------------- 180
20 --------------------- 163
30 --------------------- 146
40 ---------------------131
50 -------------------- 118
60 -------------------- 107
2) Since, the increase in time is constant, while the decrease in temperaute is not, you know that it is not linear.
3) The other two options involve exponential models.
The exponential models have a constant multiplicative rate of change, not additive. Therefore, the only feasible choice is the first one: temperature of a cup of coffee over time.
4) You can prove it:
i) Exponential models have the general form y = A [r]ˣ, where B is r is the multiplicative rate of change: any value is equal to the prior value multiplied by r:
y₁ = A [r]¹
y₂ = A[r]²
y₂ / y1 = r ← as you see this is the constant multiplicative rate of change.
ii) Test some data:
180 / 200 = 0.9
163 / 180 ≈ 0.906 ≈ 0.9
146 / 163 ≈ 0.896 ≈ 0.9
131 / 146 ≈ 0.897 ≈ 0.9
118 / 131 ≈ 0.901 ≈ 0.9
107 / 118 ≈ 0.907 ≈ 0.9
As you see all the data of the table have a relatively consistent multiplicative rate of change, which proves that the temperature follows an exponential decay; so the right choice is the first one.
