A certain isotope decays so that the amount A remaining after t years is given by: A = Ao e-0.03t where Ao is the original amount of the isotope. To the nearest year, the half-life of the isotope (the amount of time it takes to decay to half the original amount) is years.

A certain isotope decays so that the amount A remaining after t years is given by: A = Ao e-0.03t where Ao is the original amount of the isotope. To the nearest year, the half-life of the isotope (the amount of time it takes to decay to half the original amount) is years.

Name: 21 < 15 16 17 18 19 2021 2225 2627A certain isotope decays so that the
Uploaded: 2024-03-20T07:06:41.000Z
Channel: Bartleby
Description: 21 < 15 16 17 18 19 2021 2225 2627A certain isotope decays so that the amount A remaining after t years is given by:A = Ao e-0.03t where Ao is the original amount of the isotope.To the nearest year, the half-life of the isotope (the amount of time it

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter6: Exponential And Logarithmic Functions

Section6.7: Exponential And Logarithmic Models

Problem 24SE: The formula for an increasing population is given by p(t)=P0ert where P0 is the initial population...

See similar textbooks

Similar questions

Suppose that the initial mass of radioactive substance is m0 and the half-life of the substance is h. Let m(t) be the mass remaining at time t. a What is meant by the half-life h? b Write a formula for m(t) in terms of the half-life h. c Write a formula for the relative decay rate r in terms of the half-life h. d Write a formula for m(t) in terms of the relative decay rate r.
Suppose that the initial size of a population is n0 and the population grows exponentially. Let n(t) be the size of the population at time t. (a) Write a formula for n(t) in terms of the doubling time a. (b) Write a formula for n(t) in terms of the relative growth rate r.
The formula for an increasing population is given by p(t)=P0ert where P0 is the initial population and r0. Derive a general formula for the time t it takes for the population to increase by a factor of M .
In an exponential decay function, the base of theexponent is a value between 0 and 1. Thus, for somenumber b1, the exponential decay function canbe written as f(x)=a(1b)x. Use this formula, alongwith the fact that b=en, to show that an exponential decay function takes theform f(x)=a(e)nx for somepositive number n.
The formula for the amount A in an investmentaccount with a nominal interest rate r at any timet is given by A(t)=a(e)rt, where a is the amount ofprincipal initially deposited into an account thatcompounds continuously. Prove that the percentageof interest earned to principal at any time t can becalculated with the formula I(t)=ert1.