Chapter 1.1, Problem 58E

Processor Speeds The processor speed, in megahertz (MHz), of Intel processors during the period 1970-2000 could be approximated by the following function of time t in years since the start of 1970:¹⁷

$v\left(t\right)=\{\begin{array}{cc}0.12t^2+0.04t+0.2& \text{if}0\le t<12\\ 1.1{\left(1.22\right)}^t& \text{if}12\le t<26\\ 400t-10,200& \text{if}26\le t\le 30\end{array}$

a. Evaluate $v\left(2\right),v\left(12\right)$ and $v\left(28\right)$. Interpret the results.

b. Write down a technology formula for v.

c. Use technology to sketch the graph of u and to generate a table of values for $v\left(t\right)$ with $t=0,2,\dots ,30$. (Round values to two significant digits.)

d. When, to the nearest year, did processor speeds reach 500MHz?