# Graph (roughly)the exponential function using three points(draw asymptote line). Tell which one is growth? which is decay?

#1

Graph (roughly)the exponential function using three points(draw asymptote line). Tell which one is growth? which is decay? Q1. Y=2.5^(x) Q2. Y=3^(x^-2)-1 Q3. Y=2(1/3)^(x+1)+2

Answering your last two questions first. If the base fo the “x” exponential is between 0 and 1, then you have decay, because you are continually multiplying a fraction by itself. If it is greater than 1 then you ave growth.

So, #1 (base is 2.5) and #2 (base is 3) are growth and #3 (base is 1/3) is decay.

As for asymptotes for exponentials. The thing that determines the asymptote is the “x” exponential (n^x). It approaches zero when x is a really big negative number (like -99999999999999) because negative exponents mean putting the term into the denominator. Example 5^(-2) = 1/(5^2).So a really big negative exponent means a really big denominator, which is a really tiny number (but never zero).

So, if the “x” exponential term becomes nearly zero, then everything multiplied by it becomes nearly zero.

5^(-999999999999999) is nearly 0
so, 100*5^(-999999999999999) is also nearly zero.

That was for growth functions. For decays, the exact same principal applies, only the exponents that are very big POSITIVE values cause the term to approach zero.

So, that means to find the asymptote we simply act like the exponential term is zero and anything left over is the asymptote.

#1 y = 0

#2 y = 0 - 1

#3 y = 0 + 2

To graph it, you HAVE to plug in values of x and calculate values of y. Create a table and plot the points. You can use a graphing calculator or a site like