30/1 is equalivalent to
2 answers:
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Answer:
Value of the car after x years
Step-by-step explanation:
Exponential functions are generally expressed in the form: and since this function is decreasing, meaning it has an exponential decay, it can be expressed as:
where r=rate of decay.
In this case the a represents the initial value or y-intercept, since when x=0, (1-r)^0 = 1, so we just have y=a(1) or y=a
The r represents the rate of decay
the x usually represents the time in seconds, days, months, or whatever unit is being used
The y value represents the value of whatever your measuring, and in this context it represents the value of the car after x years.
This is because a represents the initial value
After one year it's only 85% worth it's initial value or 15% less which is represented as 0.85(a)
After two years it's only 85% worth the previous year or 15% less the previous year, which is represented as 0.85(0.85(a))
This will continue to decrease the number of years increase
If your directrix is a "y=" line, that means that the parabola opens either upwards or downwards (as opposed to the left or the right). Because it is in the character of a parabola to "hug" the focus, our parabola opens upwards. The vertex of a parabola sits exactly halfway between the directrix and the focus. Since our directrix is at y = -2 and the focus is at (1, 6) AND the parabola opens upward, the vertex is going to sit on the main transversal, which is also the "line" the focus sits on. The focus is on the line x = 1, so the vertex will also have that x coordinate. Halfway between the y points of the directrix and the focus, -2 and 6, respectively, is the y value of 2. So the vertex sits at (1, 2). The formula for this type of parabola is where h and k are the coordinates of the vertex and p is the DISTANCE that the focus is from the vertex. Our focus is 4 units from the vertex, so p = 4. Filling in our h, k, and p:
. Simplifying a bit gives us
. We can begin to isolate the y by dividing both sides by 16 to get
. Then we can add 2 to both sides to get the final equation
, choice 4 from above.