A ball is dropped from a certain height. The function below represents the height f(n), in feet, to which the ball bounces at the nth bounce:
f(n) = 9(0.7)n
What does the number 0.7 represent?
The ball bounces to 30% of its previous height with each bounce
The height at which the ball bounces at the nth bounce is 0.3 feet
The ball bounces to 70% of its previous height with each bounce
The height from which the ball was dropped at the nth bounce is 0.7 feet
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I think you mean
\(f(n) = 9(0.7)^n\)
If you do not use LaTeX to write the equations, you still need to write a ^ before exponents so that others know that the following digit or letter is an exponent.
You could have written f(n) = 9(0.7)^n.
The physical meaning of the various parts of this exponential equation is as follows:
h0=initial value, for example, height of ball before the first bounce (i.e. x=0)
b=ratio of (height after each bounce) / (height before bounce)
x=number of bounces.
ohh okay, and yes sorry I meant to put the n as an exponent.. I just dont know how to do this question
Not the answer you are looking for? Search for more explanations.
If you're still not sure, then calcualuate (with your calculator) the various heights of the ball after n bounces,
for n=0, the height is f(0)=9(0.7)^0
for n=1, the height is f(0)=9(0.7)^1
for n=2, the height is f(0)=9(0.7)^2
for n=3, the height is f(0)=9(0.7)^3
With the results, you can compare with the given choices to decide on which one is correct.
You can also reread my previous post and try to understand the physical meaning of the equation, after which the answer will be obvious to you.