A material transmutes 50% of its mass to another clement every 10 years due toradioactive decay. Let M, be the mass of the radioactive material at the end of the nth decade,where the initial mass of the material is Mo = 40 g.(a) Write out the first five terms of the sequence.(b) Find an explicit formula for the terms of the sequence.(c) Estimate the limit of the sequence or state that it docs not cxist.

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Answered: A material transmutes 50% of its mass…

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 formula for computing the amount of money in a savings account with an r% annual in- r t erest rate (compounded each year) t years after opening with $P is given by A(t) = P (1 + 100 o compound each year (or annually) means that the interest is computed and added to the ac- ount once a year. The interest the next year is computed on the new account value (with the revious year's interest included). 1. Eloisa plans to put $200 in a savings account with a 3.5% annual interest rate. (a) Write a function for how much money will be in the account in t years. (b) How much will be in the account after 5 years? (c) How long will it take to have $400 in the account? Explain how you found your answer.
At the beginning of the last decade, a total of 7.2 million passengers took a cruise vacation. The global cruising industry has been growing at approximately 7% per year. Assume that this growth rate continues. Suppose N = (t) gives the number of passengers, in millions, that take a cruise vacation at year t. Answer parts (a), (b), (c), and (d) of the question. Click VERIFY to move to the next part. (a) Report the following. Use the pull-down menu to indicate the units. A0) = Number Click for List (b) If (t) is written in the form a-b’, do you predict the value of b to be greater than 1 or less than 1? O b is greater than 1 O b is less than 1 (c) Complete the boxes below to write a formula which gives N as a function of t, where t is in years. Do not round any values. Since your formula gives N in millions of people, check that it passes through the initial value x = 0, N= 7.2, as opposed to passing through x = 0, y = 7,200,000. N= Number ( Number (d) How many millions of cruise…
A savings account with an interest rate r, which is compounded n times per year, and begins with P as the principal (initial amount), has the discrete nt compounding formula A (t) = P(1+)". This is n because we multiply the amount by itself plus a small amount, determined by the interest rate, and the account grows each time the compounding occurs. For continuous compounding, we use the formula A (t) = Pert , and if we have seen this formula before, we may not have gotten a satisfactory answer as to why we use it, other than some vague notion of "compounding infinity times per year". In this exercise, we'll use Bernoulli's Rule to find the connection. It might be helpful to review the "Indeterminate Powers" section of the video before beginning. Why can we write nt lim,→00 P(1+ )"t P limn¬∞ (1+)™ ? n

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