Problem

Net value after $t$ years is $N(t)=500(0.9)^t-120$ dollars. Determine the $y\text{-}\text{intercept}$ using $t=0$ and the zero-exponent rule, give the ordered pair, and interpret it as the modeled initial net value.

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Set N(t) = 0 to find the y-intercept. That procedure finds zeros, while a y-intercept is found by setting t = 0.

At t = 0, N(0) = 500(1) − 120 = 380, so the y-intercept is (0, 380): the modeled initial net value is $380.

The y-intercept is (500, 0) because 500 is the first coefficient. A y-intercept has input 0 and requires evaluating the full expression.

At t = 0, N(0) = 500 because (0.9)⁰ = 0. Any nonzero number to the zero power is 1, so the $120 must be subtracted.

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