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gracemerci1
18.10.2020 •
Mathematics
The Average home size in the United States In 1970 was 1,400 Square feet. The average size is about 5/3 times greater in 2004. What was the average size home in 2004.
Options
A: about 840 square feet
B: about 1398 square feet
C: about 1401 square feet
D: about 2333 square feet
PLEASE ANSWER ITS A TEST AND ITS DUE IN 1 1/2 HOURS
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Ответ:
Part A:
Given that the growth factor of x (the number of months) is a positive number larger than 1, we have that as the number of months increases, the price of fuel also increases
Therefore, the price of fuel A is increasing, by 4% each month
Part B:
Fuel B records a greater percentage change in price over the previous month.
Step-by-step explanation:
The function that represents the price of fuel A is f(x) = 2.96(1.04)ˣ
Where;
x = The number of months
Part A: Given that the growth factor of x (the number of months) is a positive number larger than 1, we have that as the number of months increases, the price of fuel also increases
Therefore, the price of fuel A is increasing
(2.96(1.04)² - 2.96(1.04)¹)/(2.96(1.04)¹) × 100 = 4 %
(2.96(1.04)³ - 2.96(1.04)²)/(2.96(1.04)²) × 100 = 4 %
(2.96(1.04)⁴ - 2.96(1.04)³)/(2.96(1.04)³) × 100 = 4 %
Part B: The given table is presented as follows;
Months, m
The price of fuel, g(m)
1
3.04
2
3.22
3
3.41
4
3.61
The percentage change in price for fuel A over the previous month is given as follows;
Fuel price of fuel A in the previous month f(3) = 2.96(1.04)³≈ $3.33
Fuel price of fuel A in the current month f(4) = 2.96(1.04)⁴ ≈ $3.463
The percentage change in price = (3.463 - 3.33)/3.33 × 100 ≈ 4 % change
The percentage change in price for fuel B over the previous month is given as follows;
Fuel price of fuel B in the previous month = $3.41
Fuel price of fuel B in the current month = $3.61
The percentage change in price = (3.61 - 3.41)/3.41 × 100 ≈ 5.865 % change
Therefore, fuel B recorded a greater percentage change in price of 5.865 %, over the previous month than fuel A with a percentage change in price of 4 %
Fuel B records a greater percentage change in price over the previous month.