I was wondering about a particular math problem.
It says that a particular trigonometric function, $10 \cos(2\pi x)$ models a bus going over a speed bump.
They say that the amplitude decreases over time, such that at the $x=0$ second, the amplitude is $10$ and at the first second $x=1$, the amplitude is $8$. They ask to create an exponential function just of the amplitude change, which I presume is $10 \cdot 0.8^x$.
However, they then say to use this equation to model the same cosine equation to ensure that the amplitude changes exponentially with respect to time. I thought that this would be the equation: $$10 \cdot 0.8^x \cdot \cos(2\pi x) \ ,$$ however, when I check this equation in a graph, the graph doesn't look correct.
Am I on the right track? If not, I really would appreciate all of the help I can get! Thanks so much!
The graph is below. What doesn't look right about it? The peaks decrease exponentially like you want. As the period is $2$, each peak is $0.64$ of the one before of the same sign.