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an = 52(1.06)^(n-1).

Step-by-step explanation:

After 6 years there are 70 and after 8 years there are 79 so the common ratio can be calculated:

After 6 years : a6 = a1 r^(6 - 1) = a1 r^5 and after 8 it is a1 r^(7)   where a1 is the number of raccoons in year 1.

So we have a1 r^7 / a1 r^5    

= r^2 = 79/70

r = 1.06 to the nearest hundredth.

To find the number in year 1 we have:

a1 (1.06)^5 = 70

a1 = 70 / (1.06)^5

a1 =  52 raccoons.

So an = 52(1.06)^(n-1).

Step-by-step explanation:

Part A. Using five rectangles.

I will use the left end-point approximation.

1. Divide the interval [0,20] into five equal subintervals

Δx = (20 - 0)/5 = 4

The intervals are:

[0,4], [4,8], [8,12], [12,16], [16,20]

2. Evaluate the function at the left end-points and calculate the areas

Fig. 1 shows the graph with five rectangles.

Part B. Using 10 rectangles

1. Divide the interval [0,20] into 10 equal subintervals

Δx = (20 - 0)/10 = 2

The intervals are:

[0,2], [2,4], [4,6], [6,8], [8,10], [10,12], [12,14], [14,16], [16,18], [18,20]

2. Evaluate the function at the left end-points and calculate the areas

Fig. 2 shows the graph with 10 rectangles.

Part C. The limit as n ⟶ ∞

Integrate the function.