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Find the exponential function $ f(x) = Cb^x $ whose graph is given.
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Calculus 1 / AB
Calculus 2 / BC
Functions and Models
Functions of Several Variables
Johns Hopkins University
Harvey Mudd College
University of Michigan - Ann Arbor
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.
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.
Find the exponential funct…
Exponential Functions from…
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.
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