Chapter 1.1, Problem 57E

(a)

To determine

To calculate: The value of $v\left(10\right),v\left(16\right),\text{ and }v\left(28\right)$ if the speed of the Intel processors in megahertz during the period $1980-2010$ could be modeled by the function $v\left(t\right)=\{\begin{array}{l}8{\left(1.22\right)}^t\text{ if 0}\le t\le \text{16}\\ 400t-6200\text{ if 16}\le t\le 25\\ 3800\text{ if 25}\le t\le 30\end{array}$ where t is time in years since the start of $1980$. Also, interpret the result.

(b)

To determine

The technology formula for v if the speed of the Intel processors in megahertz during the period $1980-2010$ could be modeled by the function $v\left(t\right)=\{\begin{array}{l}8{\left(1.22\right)}^t\text{ if 0}\le t\le \text{16}\\ 400t-6200\text{ if 16}\le t\le 25\\ 3800\text{ if 25}\le t\le 30\end{array}$ where t is time in years since the start of $1980$.

(c)

To determine

To graph: The sketch of v using technology and generate a table of values for $v\left(t\right)$ with $t=0,2,\mathrm{...},30$ where the function is defined by $v\left(t\right)=\{\begin{array}{l}8{\left(1.22\right)}^t\text{ if 0}\le t\le \text{16}\\ 400t-6200\text{ if 16}\le t\le 25\\ 3800\text{ if 25}\le t\le 30\end{array}$ where t is time in years since the start of $1980$.

(d)

To determine

To calculate: The time to the nearest year, when the speed of the processor reach $3$ gigahertz if the speed of the Intel processors in megahertz during the period $1980-2010$ could be modeled by the function $v\left(t\right)=\{\begin{array}{l}8{\left(1.22\right)}^t\text{ if 0}\le t\le \text{16}\\ 400t-6200\text{ if 16}\le t\le 25\\ 3800\text{ if 25}\le t\le 30\end{array}$ where t is time in years since the start of $1980$.