1. Exponential growth and decay can be expressed asA(t) = Agekt,where A(t) = the amount at time tAo = A(0), the initial amount (the amount at t = 0)k= relative rate of growth or decayt = timeThe model describes exponential growth if k isThe model describes exponential decay if k is

if k>0 , Exponential growth k,0 , Exponential decay

Answered: 1. Exponential growth and decay can be…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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The radioactive properties of the isotope technetium-99m can be used in combination with a tin compound to map circulatory disorders. Technetium-99m has a half-life of 6 hours. Write an exponential decay function that models this situation. The function p(t) should give the percent of the isotope remaining after t hours. a) a) b) Describe domain, range and the end behavior of p(t) as t increases without bound for the function found in part a. b)_ c) Write the inverse of the decay function. Use a common logarithm for your final function. c)_ d) How long does it take until 5% of the isotope technetium-99m remains? Round to the nearest tenth of the hour.
Two functions f and g are given. Show that the growth rate of the linear function is constant and that the relative growth rate of the exponential function is constant. f(t)=40+ 8.5t, g(t) = 40 e (Simplity your answer.) What is the relative growth rate of the exponential function? t/8 O A. y(t) y(t) y' (t) O c. y'(t) y' (t) y(t) What is the relative growth The relative growth rate is (Simplify your answer.) OB. O D. rate of the exponential function g(t)? which is constant.
please show all working so it can be easily understood
The decay time is the time it takes for a radioactive substance to lose half of its amount. This function is given by A(t)=a e-.69*t/Twhere a is the initial amount, t is the time elapsed, T is the time it is known to decay by one-half and A(t) is the amount left. Carbon -14 has a half-life of 5,200 years. Something is assumed to be 3500 years old. How much carbon-14 is left if it is known to have started with 20 grams of carbon-14?
1 t
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1. Exponential growth and decay can be expressed as A(t) = Apekt, where A(t) = the amount at time t A(0), the initial amount (the amount at t = 0) relative rate of growth or decay Ao k t = time The model describes exponential growth if k is The model describes exponential decay if k is