Chapter 1.1, Problem 57E

Processor Speeds The processor speed, in megahertz (MHz), of Intel processors during the period 1980-2010 could be approximated by the following function of time t in years since the start of 1980:¹⁶

$v\left(t\right)=\{\begin{array}{cc}8{\left(1.22\right)}^t& \text{if}0\le t<16\\ 400t-6,200& \text{if}16\le t<25\\ 3,800& \text{if}25\le t\le 30\end{array}$

a. Evaluate $v\left(10\right),v\left(16\right)$, 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 3 gigahertz (1 gigahertz = 1,000 megahertz), according to the model?