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

$f(x)=3 \cdot 2^{x}$

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Johns Hopkins University

Harvey Mudd College

Baylor University

University of Nottingham

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.