A fish population, \(p\), can be represented by the equation \(p= 800 \boldcdot \left(\frac{1}{2}\right)^{t}\) where \(t\) is time in years since the beginning of 2015. 

What was the fish population at the beginning of 2012?

The area, \(A\), of a forest, in acres, is modeled by the equation \(A = 5,\!000 \boldcdot \left(\frac{5}{4}\right)^d\) where \(d\) is the number of decades since the beginning of the year 1950. 

1. Is the area of the forest increasing or decreasing with time? Explain how you know.
2. What was the area of the forest in 1950? 
3. What was the area of the forest in 1940?
4. Was the area of the forest less than 1,000 acres in 1900? Explain how you know. 

A population of mosquitos, \(p\), is modeled by the equation \(p = 1,\!000 \boldcdot 2^w\) where \(w\) is the number of weeks after the population was first measured.

1. Find and plot the mosquito population for \(w = 0, 1, 2, 3, 4\).
2. Where on the graph do you see the 1,000 from the equation for \(p\)?
3. Where on the graph can you see the 2 from the equation?

The number of copies of a book sold the year it was released was 600,000. Each year after that, the number of copies sold decreased by \(\frac{1}{2}\).

The graph shows a population of butterflies, \(t\) weeks since their migration began.

Graph of a function on grid, origin O. Horizontal axis, t, weeks since migration began, from 0 to 5 by 1's. Vertical axis, q, population of butterflies, from 0 to 300,000 by 10,000's. Plotted coordinates as follows: 0 comma 250,000, 1 comma 150,000, 2 comma 90,000, 3 comma 54,000, 4 comma 32,400, 5 comma 19,440.

1. How many butterflies were in the population when they started the migration? Explain how you know.
2. How many butterflies were in the population after 1 week? What about after 2 weeks?
3. Write an equation for the population, \(q\), after \(t\) weeks.