How do you find the associated exponential decay or growth model: Q = 1,500 when t = 0; half-life = 1?

1 Answer
May 20, 2017

Start with Q(t)=Q(0)eλt
Use the fact that Q(thalf-life)Q(0)=12 to find λ

Explanation:

Start with Q(t)=Q(0)eλt [1]

At thalf-life=1

Q(1)Q(0)=12=eλ(1)

Use the natural logarithm on both sides:

ln(12)=ln(eλ(1))

Flip the equation:

λ=ln(12)

This is a better form:

λ=ln(2)

Substitute 1500 for Q(0) and ln(2) for λ into equation [1]:

Q(t)=1500eln(2)t