The amount x after t years is given by:

x(t)=x0*e^(−kt)

for some constant k. Y

We know that

x(5)=0.9*x0, so

e^(−5k)=0.9 use the natural log and solve for k

k = (-1/5) ln(0.9)

We need to find the half-life, that is, t such that

x0*e−kt=0.5*x0

e−kt=0.5

t = (-1/k) ln(0.5)

t = (1/ln(0.9))*5*ln(0.5)

t = 32.89 years

click here to see the step by step calculation

Click to see all the steps