The flight is in the shape of a parabola with a vertex 5 feet above the water and 1/2 * 33 = 16.5 feet horizontally from the point of leaving the water
y = a(x - h)^2 + k
where (h,k) is the vertex of the parabola and here it is (5 , 16.5), so we have the function:-
y = a(x - 16.5)^2 + 5
when x = 0 y = 0 so
0 = a(-16.5)^2 + 5
which gives a = -0.018365
So our function for the flight path is
y = -0.018365(x - 16.5)^2 + 5 Answer
Answer:
- x = log(y/4)/log(1.0256)
- your answer for y=12 is correct
Step-by-step explanation:
The question is asking you to solve ...
y = f(x)
for x. (In other words, find the inverse function.)
You already did this using a constant for y. Do the same thing with y instead of the constant.
y = 4(1.0256^x)
y/4 = 1.0256^x . . . . . . . divide by 4
log(y/4) = x·log(1.0256) . . . . . take logs
log(y/4)/log(1.0256) = x . . . . . divide by the coefficient of x
Now, you have a model for x in terms of y, which is what the question is asking for.
x = log(y/4)/log(1.0256) . . . . . . . exact expression
When y=12, this is ...
x = log(12/4)/log(1.0256) ≈ 43.46 . . . . weeks
_____
This is a linear equation in log(y), so can be written as such:
x = 91.0912·log(y) -54.8424 . . . . . approximate expression
P
pp is an exponential function with an initial value of
