Question
Could you please show work so I can understand the question 13. Find x as a function of z when z 3 e x =
Could you please show work so I can understand the question
13. Find x as a function of z when z3 ex = 2. Then calculate the rate of change of x with respect to z.
14. Find x as a function of y when y = y2 + ln x. Then calculate the rate of change of x with respect to y
15. Find the slope of the line tangent to y = 5x at x = 1
17. Find the maximum value of f(x) = ln(9 x2). Suggestion: first consider the domain of f.
20. Find the maximum value of f(x) = ln(1 + x x2 ) one the interval [2, 6].
21. The value of a certain machine at time t is V = 50, 000e0.08t dollars. (Here t is measured in years and t 0). At what time will the machine have a value of $10,000?
22. The value of a certain machine at time t is V = 50, 000e0.08t dollars. (Here t is measured in years and t 0). At what rate is the value changing over time?
24. The population of a certain country, in millions, at time t years is P(t) = 55e0.03t . At what rate is the population increasing with time? What is the populations relative rate of growth?
25. The capital in a certain country, in billions of dollars, at time t years is K(t) = 800e0.02t . At what rate is capital increasing with time? What is the relative rate of growth of capital?
28. The population of a certain country, in millions, at time t years is P(t) = 12e0.015t . The capital, in billions of dollars, is K(t) = 800e0.03t . Suppose that personal income is W(t) = 0.01K(t)/P(t). Is personal income increasing over time?
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