Question

Graph the exponential function f(x)=2(0.3)x

Answer 1

Answer:

The graph in the attached figure

Step-by-step explanation:

we know that

The equation of a exponential decay function is equal to

$f(x)=a(1-r)^x$

where

a is the initial value or y-intercept

r is the rate of change

we have

$f(x)=2(0.3)^x$

so

$a=2\\1-r=0.3\\r=0.70=70\%$

To graph the exponential function, find different values of f(x) for different values of x

so

For x=-1 -----> $f(x)=2(0.3)^{-1}=6.667$

For x=-0.5 -----> $f(x)=2(0.3)^{-0.5}=3.651$

For x=-0 -----> $f(x)=2(0.3)^{0}=2$

For x=0.5 -----> $f(x)=2(0.3)^{0.5}=1.095$

For x=1 -----> $f(x)=2(0.3)^{1}=0.6$

Plot the points and join them to graph the exponential function

The graph in the attached figure