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Use the Tangent feature from the DRAW menu to find the rate of change in part (b). Perriot's Restaurant purchased kitchen equipment on January 1,2014 . The val...

Question

Use the Tangent feature from the DRAW menu to find the rate of change in part (b). Perriot's Restaurant purchased kitchen equipment on January 1,2014 . The value of the equipment decreases by $15 \%$ every year. On January $1,2016,$ the value was $\$ 14,450 .$ a) Find an exponential model for the value, $V,$ of the equipment, in dollars, $t$ years after January 1 $2016 .$ b) What is the rate of change in the value of the equipment on January $1,2016 ?$ c) What was the original value of the

Use the Tangent feature from the DRAW menu to find the rate of change in part (b). Perriot's Restaurant purchased kitchen equipment on January 1,2014 . The value of the equipment decreases by $15 \%$ every year. On January $1,2016,$ the value was $\$ 14,450 .$ a) Find an exponential model for the value, $V,$ of the equipment, in dollars, $t$ years after January 1 $2016 .$ b) What is the rate of change in the value of the equipment on January $1,2016 ?$ c) What was the original value of the equipment on January $1,2014 ?$ d) How many years after January 1,2014 will the value of the equipment have decreased by half?



Answers

A tank holds 1000 gallons of water, which drains from the bottom of the tank in half an hour. The values in the table show the volume $V$ of water remaining in the tank (in gallons) after $t$ minutes.
$$ \begin{array}{|c|c|c|c|c|c|c|} \hline t(\mathrm{~min}) & 5 & 10 & 15 & 20 & 25 & 30 \\ \hline V(\mathrm{gal}) & 694 & 444 & 250 & 111 & 28 & 0 \\ \hline \end{array} $$ (a) If $P$ is the point (15,250) on the graph of $V$, find the slopes of the secant lines $P Q$ when $Q$ is the point on the graph with $t=5,10,20,25,$ and 30 (b) Estimate the slope of the tangent line at $P$ by averaging the slopes of two secant lines. (c) Use a graph of the function to estimate the slope of the tangent line at $P$. (This slope represents the rate at which the water is flowing from the tank after 15 minutes.)


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