212-5t+8 3. The value of a virtual currency (in $100) is given by V(t)= where t is the number " t²+4 of weeks since the virtual currency has been introduced. (a) Using the function given, determine the average rate of change of the virtual currency's value for (i) the first 2 weeks. (ii) from week 2 to week 4 (b) Find the instantaneous rate of change of the virtual currency's value at 2 weeks. (Round your answer to the nearest whole number) (c) What can you conclude from the results from (a) and (b)?

Use exponential regression to find the value of y when x = 50. Round your answer to the nearest whole number. 5 10 15 20 25 30 35 y 212 223 235 249 263 280 306

34) From a full 50-liter container of a 40% concentration of acid, x liters is removed and replaced with 100% acid. (a) Write the amount of acid in the final mixture as a function of x.

The daily production level is currently 100 filters and increasing by rate of 8 filters per day. (a) Estimate the change in daily production over the next week. filters (b) Estimate the daily production in a week. filters Need Help? Read It

Between the ages of 7 and 11 years, a certain boy grows 1.5 inches taller each year. At age 8, he is 50 inches tall. (a) Explain why, during this period, the function giving the height of the boy in terms of his age is linear. Since the rate of change -Select- and equals Identify the slope of this function. in/yr (b) Use a formula to express the height H of the boy as a linear function of his age A during this period. H(A) = (c) What is the initial value of the function that you found in part (b)? H(0) = , the boy's height is a linear function of time. (d) Studying a graph of the boy's height as a function of his age from birth to age 7 reveals that the graph is increasing and concave down. Does this indicate that this actual height (or length) at birth was larger or smaller than your answer to part (c)? O larger O smaller Explain your reasoning.

The graph below shows the velocity v in feet per second of a small rocket that was fired from the top of a tower at time t = 0 (t in seconds). The rocket accelerated with constant upward acceleration until its fuel was expended, then fell back to the ground at the foot of the tower. The entire flight lasted 14 seconds. 4. (4,96) t (seconds) (14,-224) (a) What was the acceleration of the rocket while its fueled lasted? (b) How long was the rocket rising? (c) What distance did the rocket travel during the time it was rising? (d) How high was the tower from which the rocket was fired? v (ft/sec)

BEAT has been selling their very own Platinum Eco-Charger since the beginning of this semester. If the number of units sold N, as a function of time, t, in years, can be represented by N(t) = 100(e-³ - e"), what was the highest number of chargers sold in a day?

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Level curves (isothermals) are shown for the water temperature (in °C) in Long Lake (Minnesota) in 1998 as a function of depth and time of year. Estimate the temperature in the lake on October 7 (day 280) at a depth of 5 m and on June 9 (day 160) at a depth of 10 m. X°C (day 280 and depth 5 m) X°C (day 160 and depth 10 m) Enter a number. Depth (m) 0 sti 10- 15+ 12 16 + 120 20 160 20 Day of 1998 16 200 240 280

Let y be the percent increase in annual US national production during a year when the unemployment rate changes by u percent. (For example, u=2 if unemployment increases from 4% to 6%.) Okun's law states that y=3.5-2u.     (a) What is the meaning of the number 3.5 in Okun's law?   (b) What is the effect on national production of a year when unemployment rises from 4% to 8%? (c) What change in the unemployment rate corresponds to a year when production is the same as the year before?Enter the exact answer as a positive value.   (d) What is the meaning of the coefficient -2 in Okun's law?