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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Answered: 1. The amount A (in grams) of a…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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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?
Suppose a radioactive substance decays at a continuous rate of 6% per year. How long will it be until only 30% of the original amount remains? Round your answer in years to the nearest hundredth (i.e., two decimal places). Enter number only, e.g. if your answer is 25.69 years, enter 25.69.
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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