Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Question

Answered step-by-step

Find the exponential function $ f(x) = Cb^x $ whose graph is given.

Video Answer

Solved by verified expert

This problem has been solved!

Try Numerade free for 7 days

Like

Report

Official textbook answer

Video by Heather Zimmers

Numerade Educator

This textbook answer is only visible when subscribed! Please subscribe to view the answer

02:46

Jeffrey Payo

Calculus 1 / AB

Calculus 2 / BC

Calculus 3

Chapter 1

Functions and Models

Section 4

Exponential Functions

Functions

Integration Techniques

Partial Derivatives

Functions of Several Variables

Johns Hopkins University

Harvey Mudd College

University of Michigan - Ann Arbor

Boston College

Lectures

04:31

A multivariate function is a function whose value depends on several variables. In contrast, a univariate function is a function whose value depends on only one variable. A multivariate function is also called a multivariate expression, a multivariate polynomial, a multivariate series, or a multivariate function of several variables.

12:15

In calculus, partial derivatives are derivatives of a function with respect to one or more of its arguments, where the other arguments are treated as constants. Partial derivatives contrast with total derivatives, which are derivatives of the total function with respect to all of its arguments.

01:07

Find the exponential funct…

0:00

01:41

01:36

01:11

Exponential Functions from…

01:55

We're looking for an exponential function that goes with the graph given, and we want it to be in this form. But what we need to do is find the value of C and the value of beat. So let's use the ordered pairs we were given and substitute them into the equation for X and Y, and we get six equals C times be to the first power when we substitute in the 0.16 and we get 24 equal See times be to the third power when we substitute in the 0.3 24 so we can use this system of equations to solve for C and B, Let's take the first equation. We know that be to the first Power is just be so we have six equals. C times be and we can isolate. See in that equation and we have C equals six divided by B. Now let's use out for a substitution and let's substitute six divided by B into the other equation where we have a seat and that gives us 24 equals six divided by B times be cubed. We can simplify that. Be cubed over B is B squared. So we have 24 equals six b squared. We can divide both sides by six and we get four equals b squared, and then we're going to square root Both sites, typically, if we square root both sides, we would write plus or minus two. But the base in an exponential function has to be positive. So we're only going to use the positive too. Okay, so now we know one of the two numbers we needed. We know the value of B. Now let's move on and find the value of C. Remember, we had see equal six Overbey. So C equals six over to soc is three. So putting all that together, we have f of X equals three times two to the X power.

View More Answers From This Book

Find Another Textbook

03:43

If you make a glass in the shape of a right circular cone (think martini gla…

01:15

The mean number of fitness magazines in a sample of homes is 16, the standar…

01:04

please helpSolve for h in U= mgh. Please show steps.

02:18

Find the area under the standard normal curve between -1.32 and the mean, P(…

06:27

In 2000, National data suggested that 26% of all U.S. businesses were owned …

02:11

Your school is planning a banquet. The cost of renting a function room is $2…

01:47

complete the identity: sec x - 1/sec x = ?

02:06

Find the absolute maximum and absolute minimum of f on the interval (-4, -1]…

02:20

A car rental is $65 per day plus $0.45 per mile travelled. Determine the equ…

03:19

Find the distance from the point (2, 3) to the line x − y = 5.