Question

How do you graph `y= 0.84( 2.01) ^ { x }`?

Answer 1

Well, we know it should be similar to the parent exponential function, `f(x) = e^x`:

Graph of `f(x) = e^x`:

graph{e^x [-10.67, 9.33, -2.48, 7.52]}

And the graph of `f(x) = (0.84)(2.01)^x` is

graph{0.84*2.20^x [-10.67, 9.33, -2.48, 7.52]}

We notice that the second graph is vertically shrunk because the graph appears wider. This comes from the fact that the function is multiplied by a value of `0.84` to expand it from the normal multiplier of `1`...

It is also slightly horizontally shrunk because the value of `2.01` is slightly less than the value of `e` (`2.7182818`).