. John and Paul are stranded on a deserted island where they survive by catching fish and picking coconuts. In one day John can catch 8 fish OR pick 12 coconuts or he can divide his time between the two in any way with no loss of efficiency. So for instance, if he spends half of the day catching fish and half picking coconuts, he can catch 4 fish AND 6 coconuts. Similarly, Paul can catch 6 fish or pick 3 coconuts in a day (and also divide time in any way between the two). Draw a PPF for John and Paul. Label the slopes and intercepts. If they want to produce 4 fish between the two of them, how may coconuts can they produce

65

step-by-step explanation:

step-by-step explanation:

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt