Samuel bought a cement mixer for $54,205. The value of the cement mixer depreciated at a constant rate per year. The table shows the value of the cement mixer after the first and second years:
Year 1 2
Value (in dollars) 47,158.35 41,027.76
Which function best represents the value of the cement mixer after t years?
f(t) = 47,158.35(0.87)t
f(t) = 54,205(0.13)t
f(t) = 47,158.35(0.13)t
f(t) = 54,205(0.87)t
The correct function that represents the value of the cement mixer after t years is:
f(t) = 47,158.35(0.87)t
The function below models the correlation between the number of hours a plant is kept in sunlight (x) and the height (y), in mm, to which it grows:
y = 4 + 2x
What does the slope of this function represent?
The original height of the plant was 4 mm.
The original height of the plant was 2 mm.
The height of the plant increases by 2 mm for every hour of sunlight it receives.
The height of the plant increases by 4 mm for every hour of sunlight it receives.
The slope of the function represents the rate of change or the increase in height for every increase of 1 in the number of hours the plant is kept in sunlight.
In this case, the slope is 2, which means that the height of the plant increases by 2 mm for every hour of sunlight it receives.
So, the correct answer is: The height of the plant increases by 2 mm for every hour of sunlight it receives.
To find the function that represents the value of the cement mixer after t years, we need to analyze the relationship between the initial value of $54,205 and the values after the first and second years.
In the first year, the value decreased from $54,205 to $47,158.35. This represents a depreciation of $54,205 - $47,158.35 = $7,046.65.
In the second year, the value decreased from $47,158.35 to $41,027.76. This represents a depreciation of $47,158.35 - $41,027.76 = $6,130.59.
We can see that the depreciation is decreasing each year, indicating that the value is decreasing at a decreasing rate. Hence, we can eliminate options that have a constant decreasing rate in their functions.
Comparing the remaining options, f(t) = 54,205(0.13)^t and f(t) = 47,158.35(0.13)^t, we can see that the second option matches our data.
Therefore, the function that best represents the value of the cement mixer after t years is f(t) = 47,158.35(0.13)^t.