the radioactive substance uranium - 240 has a...
the radioactive substance uranium - 240 has a half - life of 14 hours. the amount a(t) of a sample of uranium - 240 remaining (in grams) after t hours is given by the following exponential function. a(t)=4300(1/2)^(t/14) find the initial amount in the sample and the amount remaining after 60 hours. round your answers to the nearest gram as necessary. initial amount: grams amount after 60 hours: grams
Answer
# Explanation:
## Step1: Find initial amount
Set $t = 0$ in $A(t)=4300\left(\frac{1}{2}\right)^{\frac{t}{14}}$.
$A(0)=4300\left(\frac{1}{2}\right)^{\frac{0}{14}}=4300\times1 = 4300$
## Step2: Find amount after 60 hours
Set $t = 60$ in $A(t)=4300\left(\frac{1}{2}\right)^{\frac{t}{14}}$.
$A(60)=4300\left(\frac{1}{2}\right)^{\frac{60}{14}}\approx4300\times\left(\frac{1}{2}\right)^{4.2857}\approx4300\times0.0779\approx335$
# Answer:
Initial amount: 4300 grams
Amount after 60 hours: 335 grams