Can the formula be written in the form of an
exponential function or a power function? If not, explain why
the function does not fit either form.
2. q(x) = 5^(x^2)

Question

Can the formula be written in the form of an
exponential function or a power function? If not, explain why
the function does not fit either form.
2. q(x) = 5^(x^2)

anonymous · Answer

sorry i glitched

anonymous · Answer

a formula can be used for a power function

anonymous · Answer

other then that idk

anonymous · Answer

i know there are formulas for each but I don't know how to get into the correct form

mathmale · Answer

You've typed in:  q(x) = 5^(x^2)

which can be written using Equation Editor (below) as

$$q(x) = 5^{x ^{2}}$$

mathmale · Answer

First, Peter, from which course does this problem come?  Are you familiar with power series?

anonymous · Answer

it is from the functions modeling change book 4th addition

anonymous · Answer

and yes I know what the power function looks like

mathmale · Answer

No, Peter, not power function, but power series.  Familiar?

anonymous · Answer

i guess not then

mathmale · Answer

It just so happens that e^x can be approximated by a power series which consists of a long sum of powers of x.  
In other words, e^x is approx. equal to  1 +x/1 + x^2/2! + ...      Have you seen this form before?

anonymous · Answer

No I have not

mathmale · Answer

My point is that your  5^(x^2) can be re-written as an exponential function which in turn can be approximated by  a power series, which in turn consists of a long sum containing the first, the second, the third, (etc.) powers of x.  But if you haven't studied power series yet, it's not practical to discuss this approach.

mathmale · Answer

Can you, Peter, rewrite the given function as an exponential function?

Hint:  $$5=e ^{\log_{e}5 }$$

anonymous · Answer

one second

anonymous · Answer

$$\ln5 = \log _{e}5$$ thats as far as i can get im not sure

mathmale · Answer

5^(x^2) can be re-written as $$(e ^{\ln 5})^{x ^{2}}=e ^{x ^{2}\ln 5}$$

mathmale · Answer

I'm unsure of what to tell you next, because my suggestion here depends upon our understanding of power series expansions.  Unless I'm sorely mistaken, Peter, the last expression I've typed can be expanded in a power series.

anonymous · Answer

that will be fine thank you for the help!

mathmale · Answer

You're welcome.  If you wait a while, this question of yours may be bumped to the top of the queue and someone else may offer to help you.  Best wishes to you.

mathmale · Answer

Want me to bump you to the top of the queue now?

anonymous · Answer

sure

mathmale · Answer

OK!