In a science experiment a substance is decaying exponentially. Its mass, M grams, at time t minutes is given by M=300e^(-0.05t). Find the time taken for the mass to decrease to half of its original value.

Firstly, calculate the initial value of of M, by substituting t = 0 into the equation M=300e-0.05tInitially, M0= 300e0=300 x 1 = 300When the substance mass has decreased to half its initial value, M = 0.5 x 300 = 150.Hence, we have the equation 300e-0.05t= 150Solve: e-0.05t= 0.5-0.05t= ln 0.5t = -20ln0.5= 13.8629...= 13.9 (3 s.f.)It will take 13.9 minutes for the substance mass to decrease to half its original value.

BR
Answered by Bony R. Maths tutor

7145 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Simplify: 4log2 (3) + 2log2(5)


Integrate Cos^2(x)


How can I use the normal distribution table to find probabilities other than P(z<Z)?


What is the centre and radius of the circle with the equation x(x-2)+y(y+6)+4=0 ?


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences