Question 1

Choose the one alternative that best completes the statement or answers the question.
-The following data represent the infection rate for a particular disease in a third world country x years after a vaccine became widely available. Determine the "best" model to describe the relationship between years past and infection rate.
$\begin{array}{l|l}
\text { Years After Vaccine, } x & \text { Infection Rate (\%), y } \
\hline 1 & 32 \
2 & 11 \
3 & 5 \
4 & 2 \
5 & 0.5
\end{array}$

A) exponential model: $\mathrm { y } = 1.955 - 0.435 \mathrm { x }$
B) power model: $\hat { y } = 1.648 - 2.402 x$
C) linear model: $\hat { y } = 31.7 - 7.2 \mathrm { x }$
D) linear model: $\mathrm { y } = 31.7 + 7.2 \mathrm { x }$

Accepted Answer

The infection rates decrease rapidly from 32% to 0.5% as years increase, which suggests a rapid decline that levels off, characteristic of an exponential decay model rather than a linear or power model. The given options do not directly match typical forms of exponential decay equations (e.g., $y = ab^x$), but option A's negative coefficient for $x$ in an equation without an exponential term suggests a misunderstanding in the options provided. However, given the context and the nature of the data, an exponential model is the most appropriate choice despite the unconventional presentation in option A.

Question 2

Choose the one alternative that best completes the statement or answers the question.
-The following data represent the height (relative to the ground) of a projectile shot into the air after $x$ seconds of travel. Determine the "best" model to describe the relationship between travel time and height.
$\begin{array}{l|l}
\text { Travel Time (seconds), } & \text { Height (feet), } y \
\hline 8 & 890 \
9 & 869 \
10 & 798 \
11 & 708 \
12 & 571
\end{array}$

A) power model: $\hat { y } = 3.930 - 1.056 x$
B) exponential model: $\hat { y } = 3.354 - 0.047 \mathrm { x }$
C) linear model: $\mathrm { y } = 1566.2 - 79.9 \mathrm { x }$
D) exponential model: $\mathrm { y } = 3.354 + 0.047 \mathrm { x }$

Accepted Answer

The answer of Choose the one alternative that best completes...

Question 3

Choose the one alternative that best completes the statement or answers the question.
-The following data represent the compound yield in grams for a chemical reaction for various temperatures of the reaction. Determine the "best" model to describe the relationship between temperature and compound yield.
$\begin{array}{l|l}
\text { Temperature }\left({ }^{\circ} \mathrm{C}\right), & \text { Compound Yield (grams), } \mathrm{y} \
\hline 50 & 4 \
60 & 12 \
70 & 14 \
80 & 21 \
90 & 26
\end{array}$

A) linear model: $\mathrm { y } = - 21.7 + 0.53 \mathrm { x }$
B) exponential model: $\hat { y } = - 0.195 + 0.019 x$
C) power model: $\mathrm { y } = - 4.392 + 2.999 \mathrm { x }$
D) power model: $\hat { y } = 4.392 + 2.999 x$

Accepted Answer

The relationship between temperature and compound yield increases at a constant rate, which suggests a linear model is the best fit. The given linear model option (A) reflects a direct relationship between temperature (x) and yield (y), which aligns with the increasing trend observed in the data.

Quiz 4: Describing the Relation Between Two Variables