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1.5, Problem #6. Graph the given functions on a common grid. How are
the graphs related? What is different about them?
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| >plot([.9^x, .6^x, .3^x, .1^x],x=-5..5,y=0..6); | Using Maple, the following command would allow all plots to be made on the same axes: |
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At left is the result of the Maple plot. The order of the curves is: Red, Green, Yellow, and Blue. |
| How are the graphs related? | They all go through the point (0,1). They all are decreasing functions. They all approach the x-axis as an asymptote. |
| What is different about them? | They all have different attack angles. The smaller the base of the exponential, the steeper the attack angle. |
1.5, #16. Find the exponential function 
that goes through the points (0,2) and 
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C = 2
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We know that 
for all values of a except 0. Yet we have be given that when x
= 0, y = 2. |
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Substituting our result from the first step into the given function. |
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Substituting the given ordered pair
into our equation from the above step. |
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We algebraically solve for a. |
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We conclude that
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Because (0,2) is a point on our graph, a must be positive. |
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Now that we have found C and a, this must be our function. |
1.5, #22. Use a graph to estimate the values of x such that 
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| > plot(exp(1)^x,x=-10..20.8,y=1..1000000000); | Use Maple command for plotting natural log function. Here we must know that e is indicated as exp(1) (e to the first power). The ending position for the domain (20.8 was arrived at by trying different values until the graph appeared to go the entire way up to the top range value (the desired 1,000,000,000). |
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Here we see the resulting plot. We also see here that Maple defaults to scientific
notation for large numbers. 1e+09 means  ,
which is the 1,000,000,000 that the problem asked for. |
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