Analyze Exponential Functions

The function, $ f $, gives the number of copies a book has sold $ w $ weeks after it was published. The equation $ f(w) = 500 \cdot 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 ≤ w ≤ 2

• 0 ≤ w ≤ 7

• 5 ≤ w ≤ 7

• 5 ≤ w ≤ 10

• 0 ≤ w ≤ 10

A child asks her dad for an allowance that starts with a penny and then doubles every day for a month. Which function can be used to model the amount of money, A, the child will receive each day, x?

• A(x) = 2(0.01)^x

• A(x) = 0.01(2)^x

• A(x) = 0.01(1 - 2)^x

• A(x) = 2(1.01)^x

Which function models the values in the table?

New houses are being built in a neighborhood. The table shows the exponential change in the number of houses in the neighborhood over the last 6 years. Which exponential function best models the data?

A study was conducted to analyze the 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 · 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

Function $ f $ models the population, in thousands, of a city $ t $ years after 1930. The average rate of change of $ f $ from $ t = 0 $ to $ t = 70 $ is approximately 14 thousand people per year. Is this value a good way to describe the population change of the city over that time period?

• Yes, because it provides a simple average over the entire period.

• No, because it does not account for variations in population growth.

• Yes, because it accurately reflects the population trend.

• No, because it is not based on actual population data.

The graph shows a bacteria population decreasing exponentially over time. The equation $ p = 100,000,000 \cdot \left( \frac{2}{3} \right)^h $ gives the size of a second population of bacteria, where $ h $ is the number of hours since it was measured at 100 million. Which bacterial population decays more quickly?

• The population shown in the graph

• The population described by the equation

• Both populations decay at the same rate

• It cannot be determined from the given information

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

• 500,000

• 250,000

• 125,000

• 62,500

Technology required. A moth population, $ p $, is modeled by the equation $ p = 500,000 \cdot \left( \frac{1}{2} \right)^w $, where $ w $ is the number of weeks since the population was first measured. Use technology to graph the population and find out when it falls below 10,000.

• After 5 weeks

• After 6 weeks

• After 7 weeks

• After 8 weeks

A particular type of cell doubles in number every hour. Which function can be used to find the number of cells present at the end of h hours if there are initially 4 of these cells?

• n= 4(1/2)^h

• n= 4(2)^h

• n= 4+ (2)^h

• n= 4 + (1/2)^h