Exercise 2 Page 278

Recall that the y-intercept is the y-coordinate of the point whose x-coordinate is x=0. Therefore, to find it we just need to evaluate the exponential function y=ab^x at x=0.

y=ab^x

Substitute

x= 0

y=ab^0

ExponentZero

a^0=1

y=a* 1

MultByOne

a * 1=a

y = a

As we can see, y(0) = a. This happens because b^0 is always 1, since for an exponential function b ≠ 0. For this reason, the y-intercept of any exponential function is a.