help understanding how to graph a function

Question

I am having trouble figuring out how to graph this function. A(t) = 35e^-0.17t

When I attempted to graph it my calculator did not display anything and I am not sure how to graph it by hand.

Answer 1

I suspect the scale of your calculator when you tried to graph the function needs to be extended (zoom out).

$$A(t) = 35 e^{-0.17t} = \frac {35}{e^{0.17 t}}$$

Note that as $t \to \infty$, rather quickly, $A(t) \to 0$. In contrast, as $t$ gets smaller (as we move to the left along the "t" axis, $A(t)$ grows exponentially, and as $t \to -\infty$, $A(t) \to + \infty$. To graph manually, graph $A(0) = 35$, take just a few well-chosen positive values of $t$ and note that as those values get larger, $A(t)$ decreases toward zero. To get more of where the "action" is, test out more negative values of $t$ than positive values.

Answer 2

$$A(t) = 35e^{-0.17t}$$

• when power of $e$ becomes $0$, $A(t)=35$

• when $t$ progresses in positive direction, power of $e$ keeps on increasing in negative direction and hence value of $\left[e^{(\text{negative power})}\right]$ keeps on diminishing, but it will never become zero! (?)

• when $t$ progresses in negative direction, power of $e$ keeps on increasing in positive direction and hence value of $\left[e^{(\text{positive power})}\right]$ keeps on increasing exponentially

In the following graph red line is for $y=2^x$ and blue line is for $y=2^{-x}$