Exercise 1 Page 278

Recall that the y-intercept is the y-coordinate of the point whose x-coordinate is x=0. Therefore, the condition for our function is that y=2 when x=0. Let's review the general form of an exponential function. y=ab^xIn this form a, and b are real numbers such that a≠ 0, b> 0, and b ≠ 1. Now, let's apply the conditions we mentioned above to a function with this form.

As we can see, y(0) = 2 if we choose a=2. This happens because if b≠ 0, b^0=1. We can choose any positive value for b, as long as b ≠ 1, to obtain an exponential function that satisfies the exercise's conditions. Therefore, there are infinitely many solutions satisfying the given requirements. For example, y = 2(3)^x.