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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.

John Anthony
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  • Think of when the function will take on values that are easy to plot as individual points. If you know the general shape of the graph of an exponential function, then you can use that knowledge to connect (and extrapolate upon) the points that you plotted.

    You will need to use approximation for all values $A(t)$ except for $A(0) = 35$, assuming you use integers for $t$.

     –  Sep 10 '14 at 13:32

2 Answers2

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

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

enter image description here

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.

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

  • 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 $y=2^{-x}$ enter image description here

Vikram
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