Chapter 1.2, Problem 49E

(a)

To determine

To graph: The sketch of each model

$c\left(t\right)=6.3{\left(0.67\right)}^t$

$c\left(t\right)=0.093t^2-1.6t+6.7$

$c\left(t\right)=4.75-0.50t$

$c\left(t\right)=\frac{12.8}{t^{1.7}+1.7}$

Together with the data points in the table showing the cost of a gigabyte of hard drive storage since $2000$ and also determine the two models that best fits the data using the graph.

Year t since $2000$	Cost/Gigabyte $c\left(t\right)$ $\left(\$\right)$
$0$	$7.5$
$2$	$2.5$
$4$	$1.2$
$6$	$0.6$
$8$	$0.2$
$10$	$0.1$
$12$	$0.06$

(b)

To determine

To calculate: The lowest price in $2020$ using the model out of two models obtained in answer of part (a), where the table showing the cost of a gigabyte of hard drive storage since $2000$.

Year t since $2000$	Cost/Gigabyte $c\left(t\right)$ $\left(\$\right)$
$0$	$7.5$
$2$	$2.5$
$4$	$1.2$
$6$	$0.6$
$8$	$0.2$
$10$	$0.1$
$12$	$0.06$