Exercise 64 Page 174

We want to write an exponential function that passes through the given points. Let's consider the general form for this type of function. y=ab^x The given points must satisfy this equation. Let's substitute (2, 48) and (5, 750) into the formula. y = ab^x ⇒ 48 = ab^2 750 = ab^5 Notice that if we divide the second equation by the first, we will have an equation that we can solve for b.

Now we can start writing our equation. y=a b^x ⇒ y=a( 2.5)^x To find the value of a, let's substitute the point (2, 48), this time into our partial equation.

Finally, we can write the full equation of the exponential function. y= a(2.5)^x ⇒ y= 7.68(2.5)^x