A retirement account growing at an exponential rate is expected to double in 14 years. Write an equation for the amount in the account after t years in terms of the starting contribution, assuming no further contributions. Be sure to give units for all constants.
A dart lands uniformly somewhere in the triangle bounded by the x-axis, the y-axis and the line 5x + 2y = 10. Compute the probability density of the location of the dart.
A revenue forecast for a technological innovation forecasts earnings of n^(?2/5) million dollars in year n. (a) Express the total possible earnings of this innovation (assuming you can continue marketing it forever) as an infinite series in Sigma-notation.
Write a differential equation for this scenario. You do not have to solve the differential equation but you must give the interpretation of all variables and constants, their units, and indicate which is the dependent and the independent variable. The amount of an endowment increases due to investment at a rate proportional to the value, decreased by fees that are taken out at a constant rate.
Let g(x) be the time in hours it takes to drill a one foot diameter shaft x meters deep into a bed of limestone. State an interpretation for the inverse function g?1.
Find a function $g(x)=c x^{p}$ such that $f(x) \sim g(x)$ as $x \rightarrow \infty$ where $$ f(x)=\frac{\sqrt{4 / x}}{\frac{3}{x}+\frac{5}{x^{2}}} . $$ You do not have to prove your answer but we should be able to see how you got it.
The price of a turkey is proportional to its weight and inversely proportional to the square of its age. Jack’s mother gives him enough money to buy a 10 pound turkey that is one year old. When Jack gets to the fair, he realizes that he needs a turkey that is slightly bigger. How much older will the turkey have to be per extra pound in weight? Please begin by writing down an equation satisfied by price, weight and age, giving the interpretation and units for all varialbles and constants used.
An estuary contains 10 kg. of PCB (toxic waste) dispersed in a total of 3 MCF (million cubic feet) of mud. Influx of muddy water will add to the mud volume at the rate of 1 MCF / year. Superfund begins to clean up the site using an enzyme that breaks down (hence removes) the PCB at a rate proportional to the concentration in kg/MCF of PCB. Write an initial value problem for the amount P (t) of PCB present af- ter t years. Be sure to state interpretations and units for any constants you introduce.
“Dollar Bill” Stearn was convicted of tax evasion. As of January, 2017, he owed the U.S. Treasury a total of $14 million in back taxes. The payment agreement requires him to pay back $1.5 million each year on January 1, beginning in 2018. Federally mandated interest charges add 10% to his bill every December 31. (a) How many millions of dollars does he owe on the morning of January 2 of each of these years?
Write AC or CC or D to indicate whether the given series is Absolutely Convergent or Conditionally convergent or Divergent. \sum_{n=1}^{infty} (2^(2n) + (-5)^n)/5^n
