A sample of 600 grams of radioactive substance decays according to the function A(t)=600e^-0.045t where t is the time in years. How much of the substance will be left in the sample after 20 years? Round to the nearest whole gram.
A 778 g
B 1 g
C 0 g
D 244 g
Just plug in 20 for t in the equation
To find out how much of the substance will be left in the sample after 20 years, we need to substitute the value of t into the decay function A(t) and solve for A(20).
Given:
A(t) = 600e^(-0.045t)
t = 20 years
Substituting the values:
A(20) = 600e^(-0.045(20))
Simplifying the expression:
A(20) = 600e^(-0.9)
Using a calculator, we can find the value of e^(-0.9) to be approximately 0.407.
Now we can substitute this value back into the equation:
A(20) = 600 * 0.407
Calculating this, we get:
A(20) â 244.2
Rounding to the nearest whole gram, there will be approximately 244 grams of the substance left in the sample after 20 years. So the answer is D) 244 g.
To find out how much of the substance will be left after 20 years, we can use the given function A(t) = 600e^(-0.045t) and substitute t = 20 into the function.
A(20) = 600e^(-0.045 * 20)
First, we calculate -0.045 * 20 = -0.9.
A(20) = 600e^(-0.9)
Next, we evaluate e^(-0.9). Using a calculator, we find e^(-0.9) â 0.406.
A(20) = 600 * 0.406
Now, we multiply 600 by 0.406 to get the final answer:
A(20) â 243.6 grams
Rounding this to the nearest whole gram, we get 244 grams.
Therefore, the answer is D. 244 g.