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If K dollars are charged now to a credit card on which interest is p% per year, then after t years, the balance will have grown to K(t)= K(1+ (p/100))^t
(a) Using linearization, show that ln(1 + (p/100) ) ≈ p/100 . (p is an interest rate, so p/100 is reasonably small)
(b) Derive the approximation ln(Kt) ≈ ln(K) + pt /100
(c) Approximate the percentage interest rate at which the balance doubles after 9 years. (your answer to (c) will contain a term involving ln(2))
If 309 students was enrolled in a weekend and evening program, or a regional center with 6,633 students what is the probability of a randomly selected student attended a regional center or the weekend and evening program?
COST OF REMOVING TOXIC POLLUTANTS . The cost, measured in millions of dollars, of removing x% of a toxic pollutant is given.
Create an activity (e.g., a worksheet, a computer program, etc) that uses mathematical modeling of another context. Identify the Common Core State Standards content standards that your activity addresses. Provide solutions for your activity.
Suppose that the firm sells all its output at a price per unit of $24 for A and $12 for B. Find the daily production levels x and y that maximize profit.
One poll found that 46% of male voters will support a candidate while another found that 49% of female voters will be in support. To test whether this candidate has equal levels of support between male and female voters, what should the alternative h..
Let f(x,y) be an infinitely differentiable function. Suppose that Consider the surface z = f(x,y). Show that K(0,0) = f_xx(0,0) f_yy(0,0) - f_xy(0,0)^2.
Determine the optimal shipments between the European ports and the warehouses and the distribution centers to minimize total transportation costs
Find the equation of the line tangent to the curve of y = x2 ln x at the point (1,0).
What is the difference between the critical-value method and the p-value method of hypothesis testing?
students in an english class took a final exam. they took equivalent forms of the exam at monthly intervals thereafter.
Solve the systems of equations .It is necessary to set up the appropriate equations. All numbers are accurate to at least three significant digits.
The graph of dy/dt against t is in Figure. The three shaded regions each have area 2. If y = 0 when t = 0, draw the graph of y as a function of t.
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