Question

Order the functions by growth rate.

a. (x) = 50⁷ . 2300
b. (x) = 6x²
c. (x) = 55x!
d. (x) = 9x

Answer 1

To order the functions by growth rate, we compare their rates of increase. The exponential function has the highest growth rate, followed by the quadratic function, linear function, and constant function.

Step-by-step explanation:

To order the functions by growth rate, we need to compare the rates at which the functions increase as x increases.

1. Function (x) = 55x! is an exponential function. Exponential functions grow at a faster rate than polynomials, so this function has the highest growth rate.
2. Function (x) = 6x² is a quadratic function. Quadratic functions grow at a slower rate than exponential functions but faster than linear functions.
3. Function (x) = 9x is a linear function. Linear functions grow at a constant rate, so this function has the slowest growth rate.
4. Function (x) = 50⁷ . 2300 is a constant function. Constant functions do not change with the input, so this function has no growth rate.