Problem 67
A superball dropped from the top of the Washington Monument ( 556 ft high) rebounds three-fourths of the distance fallen. How far (up and down) will the ball have traveled when it hits the ground for the 6 th time?
Problem 70
Suppose you accepted a job for the month of February \((28\) days) under the following conditions. You will be paid \(\$ 0.01\) the first day, \(\$ 0.02\) the second, \(\$ 0.04\) the third, and so on, doubling your previous day's salary each day. How much would you earn?
Problem 89
The sequence \(1,4,9,16, \ldots\) can be written as \(f(x)=x^{2}\) with the domain the set of all positive integers. Explain how the graph of \(f\) would compare with the graph of \(y=x^{2}\)
Problem 91
The sides of a square are each \(16 \mathrm{cm}\) long. A second square is inscribed by joining the midpoints of the sides, successively. In the second square, we repeat the process, inscribing a third square. If this process is continued indefinitely, what is the sum of all of the areas of all the squares? (Hint: Use an infinite geometric series.) (IMAGE CANNOT COPY)
Problem 102
A single cell of bacterium divides into two every 15 min. Suppose that the same rate of division is maintained for 4 hr. Give a sequence that lists the number of cells after successive \(15-\min\) periods.