Lesson 10

A store receives 2,000 decks of popular trading cards. The number of decks of cards is a function, \(d\), of the number of days, \(t\), since the shipment arrived. Here is a table showing some values of \(d\).

A study was conducted to analyze the effects on deer population in a particular area. Let \(f\) be an exponential function that gives the population of deer \(t\) years after the study began.

If \(f(t)=a \boldcdot b^t\) and the population is increasing, select all statements that must be true.

\(b>1\)

\(b<1\)

The average rate of change from year 0 to year 5 is less than the average rate of change from year 10 to year 15.

The average rate of change from year 0 to year 5 is greater than the average rate of change from year 10 to year 15.

\(a > 0\)

The function, \(f\), gives the number of copies a book has sold \(w\) weeks after it was published. The equation \(f(w) = 500 \boldcdot 2^w\) defines this function.

Select all domains for which the average rate of change could be a good measure for the number of books sold.

\(0 \leq w \leq 2\)

\(0 \leq w \leq 7\)

\(5 \leq w \leq 7\)

\(5 \leq w \leq 10\)

\(0 \leq w \leq 10\)

Technology required. A moth population, \(p\), is modeled by the equation \(p = 500,\!000 \boldcdot \left(\frac{1}{2}\right)^w\), where \(w\) is the number of weeks since the population was first measured.

1. What was the moth population when it was first measured?
2. What was the moth population after 1 week? What about 1.5 weeks? 
3. Use technology to graph the population and find out when it falls below 10,000. 

Give a value for \(r\) that would indicate that a line of best fit has a positive slope and models the data well.

The size of a district and the number of parks in it have a weak positive relationship.

Explain what it means to have a weak positive relationship in this context.