The function is:
W(x)=740× # 0.87 # ^x
This is an exponential decay function because the base 0.87is between 0 and 1:
0 < 0.87 < 1
That means the sample's weight decreases over time.
We need to find the weight when:
x=3
Substitute 3into the function:
W(3)=740× # 0.87 # ^3
First calculate the exponent:
# 0.87 # ^3=0.87×0.87×0.87
# 0.87 # ^3=0.658503
Now multiply by 740:
W(3)=740×0.658503
W(3)=487.29222
Rounded to two decimal places:
W(3)#487.29
So the weight of the radioactive sample after 3 years is approximately:
487.29 " oz. "