The exponential function that gives the relationship between y and t is:
.
An increasing exponential function is modeled by:
In which:
In this problem, the parameters are given as follows:
A(0) = 370000, r = 0.06.
Hence the equation is:
More can be learned about exponential functions at brainly.com/question/25537936
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Answer:
<u>Assunming that the equation is y = -16x² +85x, I suggest Dario find a new profession. He kicks the ball 133 feet high, but it only travels 2.7 feet downfield at that point. It will have travelled 2*2.7 feet or 5.4 feet horizontal when it returns to ground.</u>
Step-by-step explanation:
We can answer the question of how hiogh and far the ball travels (in feet) by either of two methods. The first is to differentiate the equation and set it equal to 0, and the second is the graph it and look for the vertex and x intercept.
<u>Differentiate</u>
y = -16x² +85x
The first derivative produces an equation that gives us the slope of the line at any point x. At the ball's top height, it stops and reverses direction, a point at which the slope is zero.
y = -16x² +85x
d(y)/d(x) = -32x + 85
0 = -32x + 85
32x = 85
x = 2.66 feet horizontal distance when the ball reaches its peak.
At x = 2.66, y is 112.9 feet high
When the ball returns, it adds amnother 2.66 feet to the horizontal distance, for a total of 5.4 feet.
Graph:
See attached plot of the function.
Horizontal distance is 2.66 feet and height is 133 feet. The x-intercept is at 5.4 feet.
After all that, the ball only travelled downfield (we hope downfield) a total of 5.4 feet.
