Chapter 1.1, Problem 58E

(a)

To determine

To calculate: The value of $v\left(2\right),v\left(12\right),\text{ and }v\left(28\right)$ if the speed of the Intel processors in megahertz during the period $1970-2000$ could be modeled by the function $v\left(t\right)=\{\begin{array}{l}0.12t^2+0.04t+0.2\text{ if 0}\le t\le \text{12}\\ 1.1{\left(1.22\right)}^t\text{ if 12}\le t\le 26\\ 400t-10,200\text{ if 26}\le t\le 30\end{array}$ where t is time in years since the start of $1970$. Also, interpret the result.

(b)

To determine

The technology formula for v if the speed of the Intel processors in megahertz during the period $1970-2000$ could be modeled by the function $v\left(t\right)=\{\begin{array}{l}0.12t^2+0.04t+0.2\text{ if 0}\le t\le \text{12}\\ 1.1{\left(1.22\right)}^t\text{ if 12}\le t\le 26\\ 400t-10,200\text{ if 26}\le t\le 30\end{array}$ where t is time in years since the start of $1970$.

(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 $v\left(t\right)=\{\begin{array}{l}0.12t^2+0.04t+0.2\text{ if 0}\le t\le \text{12}\\ 1.1{\left(1.22\right)}^t\text{ if 12}\le t\le 26\\ 400t-10,200\text{ if 26}\le t\le 30\end{array}$ where t is time in years since the start of $1970$.

(d)

To determine

To calculate: The time to the nearest year, when the speed of the processor reaches $500$

MHz if the speed of the Intel processors in megahertz during the period $1970-2000$ could be modeled by the function $v\left(t\right)=\{\begin{array}{l}0.12t^2+0.04t+0.2\text{ if 0}\le t\le \text{12}\\ 1.1{\left(1.22\right)}^t\text{ if 12}\le t\le 26\\ 400t-10,200\text{ if 26}\le t\le 30\end{array}$ where t is time in years since the start of $1970$.