The processor speed, in megahertz, of Intel processors could be approximated by the function of time t in years since the start of 1995. $$P ( t ) = \left\{ \begin{array} { l l }
75 t + 200 & \text { if } 0 \leq t \leq 4 \
600 t - 1,900 & \text { if } 4

Question

The processor speed, in megahertz, of Intel processors could be approximated by the function of time t in years since the start of 1995.   $$P ( t ) = \left\{ \begin{array} { l l } 
75 t + 200 & \text { if } 0 \leq t \leq 4 \
600 t - 1,900 & \text { if } 4 < t \leq 9
\end{array} \right.$$ 
Use the model to estimate when processor speeds first hit 3.2 gigahertz (1 gigahertz = 1,000 megahertz).

A) $t = 8.2$
B) $t = 9.0$
C) $t = 6.5$
D) $t = 8.5$
E) $t = 8.8$

Quizplus · Accepted Answer

To find when processor speeds first hit 3.2 gigahertz (or 3200 megahertz), we need to set $P(t) = 3200$ and solve for $t$. Since 3200 megahertz is a high speed, it's likely in the second part of the piecewise function. So, we use the second equation:$$600t - 1900 = 3200$$Solving for $t$:$$600t = 5100$$$$t = 8.5$$Therefore, the processor speeds first hit 3.2 gigahertz 8.5 years after the start of 1995.