Which of the following options results in a graph that shows exponential growth?
f(x) = 0.4(3)x
f(x) = 3(0.5)x
f(x) = 0.8(0.9)x
f(x) = 0.9(5)−x
To determine which of the given options results in a graph that shows exponential growth, we need to remember the general form of an exponential function, which is f(x) = ab^x. Here, a represents the initial value or y-intercept, and b represents the growth factor.
Let's analyze each option:
f(x) = 0.4(3)^x:
In this case, a = 0.4 and b = 3. Since the base (b) is greater than 1, this function represents exponential growth.
f(x) = 3(0.5)^x:
Here, a = 3 and b = 0.5. Since the base (b) is between 0 and 1, this function represents exponential decay, not growth.
f(x) = 0.8(0.9)^x:
For this function, a = 0.8 and b = 0.9. Similar to the previous case, the base (b) is between 0 and 1, resulting in exponential decay, not growth.
f(x) = 0.9(5)^−x:
In this example, a = 0.9 and b = 5^(-1). Simplifying, b = 1/5, which is between 0 and 1. Hence, this function represents exponential decay as well.
From the analysis above, only the option f(x) = 0.4(3)^x results in a graph that shows exponential growth.
to write
5 to the third power you type
5^3
so maybe I am guessing the first one might be
f(x) = .4* 3^x ???
that would be like
.4*3
.4*9
.4*27 etc, growing exponentially
----------------------
however
3 * .5^x
would be like
3 * .5
3 * .25
3 * .125
sinking like a rock
same for .9^x
now
.9 * 5^-x
would be like
.9 * 1/5
.9 * 1/25
.9 * 1/125
sinking even faster