++ ATOT official NEF thread part IV ++

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My math homework. Didn't have time to really delve into #4, or I just didn't get it. Enjoy.

Math 111

Section 4.3 Questions:
1)Explain, in basic terms, what it means to be an exponential function.
An exponential function is a function where the exponent is the unknown variable, as opposed to the functions we’ve seen in the past where the unknown number (variable) has has a defined exponent attached.
2)Explain the difference between a power function and an exponential function.
Similar to the response in the previous question, a power function is represented as a variable being raised to specific power (f(x)=x^2) and an exponential function is a defined number that is greater than one being raised by a power of an unknown number. (f(x)=16^x)
3)Explain how to find the average rate of change. In comparison, explain what it means to
find the ratio of consecutive outputs.
To find the average rate of change, you must divide the change in y by the change in x. ((∆y)/(∆x)). This will give you a defined number if the equation is rational. To find the ratio of consecutive outputs, you must find the average rate of change between consecutive x values on the graph, and then divide the second defined number by the first defined number, and that ratio (and potentially whole number) is the ratio of consecutive outputs. This value is doesn’t have to be constant.

4)For the function f(x) seen in example 3, answer the following.
Please explain what this notation means and provide your answer in a complete
sentence.

5)List the similarities of the graphs f(x)=a^x for a>1 and the other when graph for 0<a<1.
The similarities between the two (a^x for a>1 and a^x for 0<a<1) are that both have no horizontal intercepts, a single y intercept, a horizontal asymptote of x equals zero, is one-to-one, smooth, continuous. The both have a domain from negative inifinity to iinfinity and a range of zero to infinity.
6)List the differences of the graphs f(x)=a^x for a>1 and the other graph when for 0<a<1.
The differences between between the two (a^x for a>1 and a^x for 0<a<1) is that a^x for a>1 is increasing as x values get larger and the horizontal asymptote is going towards negative infinity, while a^x for 0<a<1 is decreasing as x intervals get larger and that the horizontal asymptote is getting closer as positive infinity nears.
7) What is the approximate value of e?
The approximate value of e is 2.7182818284
It is found by starting with 1, then 1 divided by 1, then 1 divided by 1 multiplied by 2, then 1 divided by 1 multiplied by 2 multiplied by 3, and so on. It&#8217;s quite useful for calculating (compound) interest and other events that take place in a defined, chronological order.
 

shortylickens

No Lifer
Jul 15, 2003
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This dude has mad skills.



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