Question

Identifying Exponential Growth Functions Which is an exponential growth function? f(x) = 6(0.25)x f(x) = 0.25(5.25)x f(x) = –4.25x f(x) = (–1.25)x

Answer 1

Answer:

f(x) = 0.25(5.25)ˣ

Step-by-step explanation:

In order to show exponential growth, the numbers must be positive and the base of the exponent must be larger than 1.

Think of it as a percentage.  The base of the exponent will be the percentage of the original amount taken each time; if it is less than 1.00 then it would shrink.  Larger than 1.00 will grow.  The only one with positive numbers and a growth factor of greater than 1 is f(x) = 0.25(5.25)ˣ.

Answer 2

The exponential growth function is $\boxed{f\left( x \right) = 0.25 \times {{\left( {5.25} \right)}^x}}$. Option (b) is correct.

Further explanation:

Given:

The options are as follows,

(a). $f\left( x \right) = 6{\left( {0.25} \right)^x}$

(b). $f\left( x \right) = 0.25{\left( {5.25} \right)^x}$

(c). $f\left( x \right) = {\left( { - 4.25} \right)^x}$

(d). $f\left( x \right) = {\left( { - 1.25} \right)^x}$

Explanation:

The general form of exponential function can be expressed as follows,

$f\left( x \right) = a \times {\left( {b} \right)^x}$

Here, $a$ represents the initial value, $f\left( x \right)$ is the value after time $x$ and $b$ represents the growth rate.

For exponential grown function the value of b must be greater than 1.

In option (a) value of $b$ is less than 1. Therefore, it doesn’t represent the exponential growth.

In option (b) value of $b$ is greater than 1. Therefore, itrepresents the exponential growth.

In option (c) value of $b$ is less than 1. Therefore, it doesn’t represent the exponential growth.

In option (d) value of $b$ is less than 1. Therefore, it doesn’t represent the exponential growth.

The exponential growth function is $\boxed{f\left( x \right) = 0.25 \times {{\left( {5.25} \right)}^x}}$. Option (b) is correct.

Learn more:

1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.
2. Learn more about equation of circle brainly.com/question/1506955.
3. Learn more about range and domain of the function brainly.com/question/3412497

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Exponential function

Keywords: population grow, rate of growth, growth model, exponential growth, estimates, t years, exponential growth model, standard form, point slope form, exponential function.