Answered: Given the following exponential…

Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease. y = 210(1.09)"

Intermediate Algebra

19th Edition

ISBN:9780998625720

Author:Lynn Marecek

Publisher:Lynn Marecek

Chapter10: Exponential And Logarithmic Functions

Section10.2: Evaluate And Graph Exponential Functions

Problem 125E: What happens to an exponential function as the values of x decreases? Will the graph ever cross the...

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Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

Given the following exponential function, identify whether the change represents
growth or decay, and determine the percentage rate of increase or decrease.
y = 210(1.09)"

Expert Solution

Step 1

Given data:

The given expression is y=210(1.09)^x.

The given expression can be written as,

$y = 210 {(1 + 0.09)}^{x}$

The standard expression for the exponential function is,

$\begin{array}{rcl} y & = & a {(1 + r)}^{x} \end{array}$

Compare the given expression with the above expression.

$\begin{array}{rcl} a & = & 210 \\ r & = & 0.09 \\ = & 9 % \end{array}$

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