1. The amount A (in grams) of a radioactive substance decays so that we can always gettomorrow's amount by multiplying today's amount by 0.75. A lab experiment starts withgrams.a. Give the exponential model that would represent the amount of this substance A afterdays in this situation.b. What is the percent decay rate of this radioactive substance?c. How much radioactive substance is left after 12 days? Round to 2 decimals and includeappropriate label. A(}):Lo9.075)=03 grams2. A TikTok with 3240 views starts to go viral, with views increasing at a rate of 27% perhour.a. Write an exponential function to model v, the number of views on this TikTok after hhours.b. How many views will this TikTok have in 9 hours? Round your answer to the nearestwhole number and include appropriate label.v(n)%3324010-2)^c. How long will it take to reach 400,000 views? Round to 2 decimal places and include arappropriate label.3. The population Pof a college tyears after 2009 is given by P(t) = 9480(1.039)*%3Da. What is the percent growth rate of this population?b. According to this model, in what calendar year will this city's population reach 17,000?

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Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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3. You have the information that the number of cases of influenza on Dec 31 (day 0) was 29 and on day 5 there were 32 cases. Define variables: t = time in days since Dec 31C = number of cases a. Assume this situation is linear. Write a formula for this situation. C=·t+29 c. Assume this situation is exponential. Write a formula for this situation. d. Use your exponential formula to determine when the number of cases will hit 128
4. The Jones experienced a lot of snow this year. On Saturday, the snow was falling at the exponential rate of 10% per hour. The Jones originally had 2 inches of snow. a. Write an exponential equation that models the inches of snow, S, on the ground at any given hour, b. (Recall that in general the exponential equation takes on the form of A = Ageht) Use the correct variables. S= b. If the snow began at 8 A.M. on Saturday and the Jones are expected home Sunday at 9 P.M., approximately how many feet of snow rounded to the nearest feet, will they have to shovel from their driveway? Is this enough to cancel school on Monday? c. After about how many hours, will the snow be at least 2 feet? (Hint: 'e' can be found on your calculator right above the 'In' function key. Be careful with conversion factors, inches in 1 foot).
10. Which function represents exponential growth? O A. y = 16(0.4)" %3D B. y= 823 %3D C. 20 2 O D. y = 20 8.
A. you have an exponential function with an a-value (starting amount) of 2 and a b-value (rate) of 1.2. What is the equation? B. take the equation form question #1 and move it 3 clicks to the left. What is the new equation? C. take your answer from C and move it down 5 clicks. What is the new equation?
6. An average earthquake measures 4.5 on the Richter scale. a. How much more intense is an earthquake that measures 8.5 on the Richter scale? b. What is the magnitude of an earthquake that is 200 times more intense than an average earthquake? M = log I
Ford O D. -5.5 werPo 7. Suppose you deposit $1000 in an account paying 3% annual interest, compounded continuously. Use A = Pe to find the balance after 10 years. O A. $1349.86 This P B. $1068.65 C. $20,085.54 My Technici D. $1300
9. A new car is purchased for $22,627. Each year, the car decreases in value by 3.1%. a. Write an exponential function for the value of the car using time (t) in years as the input quantity. b. How much is the car worth in 5 years? Use your equation from part a to solve. Round to two decimal places.
A car has a purchase price of $24,800. The value declines continuously at an exponential rate of %23 annually. A. Wat is an equation modeling the value of this car after t years? B. What is its value after 6 years? c. How long will it take for its value to be $2000? 2. A bacteria colony grows continuously at an exponential rate. There are initially 1.1 million sent. After 5 days, there are 6.8 million present . a. What is the an equation modeling the number of bacteria present after d days? b. How many bacteria will be present after 7 days? c. How long will it take the number of bacteria to reach 92 million?
22. The population of a rural community was 3050 in 2010 and the population had increased to 3500 in 2015. Assuming exponential growth find the following. a. The growth rate to 4 decimal places and as a percentage. b. Estimate the population in 2018 if the trend continues.
4.4

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