Question

Decide if the function is an exponential growth function or exponential decay function, and describe its end behavior using limits. Y=7^-x

Answer 1

Answer with explanation:

The exponential function is

    $y=7^{-x}=\frac{1}{7^x}$

If you plot the function on the coordinate plane, you will find that function is decreasing function,that is when x increases ,f(x) decreases.

It is a decreasing function,because, for

 $x_{1}>x_{2}\\\\ y_{1}$

The Curve has one  Asymptote which is, y=0.

$\lim_{x \to \infty} y= \lim_{x \to \infty} 7^{-x} =0$

As, x→∞,

$7^{-x}=\frac{1}{7^x}\\\\=\frac{1}{7^{\infty}}\\\\=\frac{1}{\infty}=0$

So, when , x→∞,y→0.

It is an exponential decay function.

Answer 2

Answer:

Exponential Decay

Its end behavior on the left is as follows as x approaches negative infinity y approaches positive infinity. Its end behavior on the right is as follows as x approaches positive infinity y approaches negative infinity.

Step-by-step explanation:

We can graph the function by graphing two points when x=0 and x=1.

x=0 has $y=7^{-x} =7^{0} =1$

x=1 has y=$7^{-x} =7^{-1} =\frac{1}{7}$

This function starts with higher output values and decreases over time. This is Exponential Decay. Its end behavior on the left is as follows as x approaches negative infinity y approaches positive infinity. Its end behavior on the right is as follows as x approaches positive infinity y approaches negative infinity.