Answer:
The function, f(x) to model the value of the van can be expressed as follows;
![f(x) = 32,500 \times \left(0.88\right)^x](https://tex.z-dn.net/?f=f%28x%29%20%3D%2032%2C500%20%5Ctimes%20%5Cleft%280.88%5Cright%29%5Ex)
Step-by-step explanation:
From the question, we have;
The amount at which Amrita bought the new delivery van, PV = $32,500
The annual rate of depreciation of the van, r = -12% per year
The Future Value, f(x), of the van after x years of ownership can be given according to the following formula
![f(x) = PV \cdot \left(1 + \dfrac{r}{100} \right)^x](https://tex.z-dn.net/?f=f%28x%29%20%3D%20PV%20%5Ccdot%20%5Cleft%281%20%2B%20%5Cdfrac%7Br%7D%7B100%7D%20%5Cright%29%5Ex)
Therefore, the function, f(x) to model the value of the van after 'x' years of ownership can be expressed as follows;
![f(x) = 32,500 \cdot \left(1 - \dfrac{12}{100} \right)^x = 32,500 \cdot \left(0.88\right)^x](https://tex.z-dn.net/?f=f%28x%29%20%3D%2032%2C500%20%5Ccdot%20%5Cleft%281%20-%20%5Cdfrac%7B12%7D%7B100%7D%20%5Cright%29%5Ex%20%3D%2032%2C500%20%5Ccdot%20%5Cleft%280.88%5Cright%29%5Ex)
Answer:
-2/3
Step-by-step explanation:
The only way the answer could be one is if the exponent is 0
So 3x-2=0:
3x = -2
x = -2/3
Hope this helps!
Answer:
y=-3/7x+2
Step-by-step explanation:
first formula (Slope): y2-y1/x2-x1
-1-2/7-0= -3/7
second formula (point slope): y-y1=m(x-x1)
y-2=-3/7(x-0)
(distribute the -3/7)
y-2=-3/7x-0
(add 2 to both sides)
y=-3/7x+2
Answer:
Exponential
Step-by-step explanation:
Linear is easy to remember because it goes in a straight LINE.
Only other option is a quadratic and this does not create a parabola
Answer:
B)max/ opens down
Step-by-step explanation:
Parabola equation:
The equation of a parabola has the following format:
![y = ax^2 + bx + c](https://tex.z-dn.net/?f=y%20%3D%20ax%5E2%20%2B%20bx%20%2B%20c)
If
, that is, x² is multiplied by a positive number, the function has a minimum value and the parabola opens up.
If
, that is, x² is multiplied by a negative number, the function has a maximum value and the parabola opens down.
In this question:
![y = -x^2 - 2x + 3](https://tex.z-dn.net/?f=y%20%3D%20-x%5E2%20-%202x%20%2B%203)
From the graph, we already see that it opens down and has a max, and analitically, since
, this is confirmed. The correct answer is given by option b.