BackCompounded inflation The U.S. government reports the rate of inflation (as measured by the consumer index) both monthly and annually. Suppose for a particular month, the monthly rate of inflation is reported as 0.8%. Assuming this rate remains constant, what is the corresponding annual rate of inflation? Is the annual rate 12 times the monthly rate? Explain.
Chemotherapy In an experimental study at Dartmouth College, mice with tumors were treated with the chemotherapeutic drug Cisplatin. Before treatment, the tumors consisted entirely of clonogenic cells that divide rapidly, causing the tumors to double in size every 2.9 days. Immediately after treatment, 99% of the cells in the tumor became quiescent cells which do not divide and lose 50% of their volume every 5.7 days. For a particular mouse, assume the tumor size is 0.5 cm³ at the time of treatment.
d. Plot a graph of V(t) for 0 ≤ t ≤ 15. What happens to the size of the tumor, assuming there are no follow-up treatments with Cisplatin?
Rule of 70 Bankers use the Rule of 70, which says that if an account increases at a fixed rate of p%/yr, its doubling time is approximately 70/p. Use linear approximation to explain why and when this is true.
In Exercises 5 and 6, solve for t.
6. ln(t-2) = ln8 - ln(t)
In Exercises 1–4, solve for t.
1. a. e^(-0.3t) = 27
In Exercises 1–4, solve for t.
1. c. e^((ln 0.2)t) = 0.4
In Exercises 1–4, solve for t.
2. b. e^(kt) = 10
In Exercises 1–4, solve for t.
e^(sqrt(t)) = x^2
In Exercises 79–84, solve for y.
79. 3^y = 2^(y+1)
In Exercises 79–84, solve for y.
81. 9e^(2y) = = x^2
In Exercises 79–84, solve for y.
83. ln(y-1) = x + ln(y)
13. For what x>0 does x^(x^x) = (x^x)^x? Give reasons for your answer.