Suppose a radio active substance decays at a rate of 3.5% per hour. First write an exponential decay function that describes a quantity of radio active substance that starts at 100. Then determine how much is left after 6 hours? Round to the nearest hundredth.
y = 100(.965)^x is the equation?
y = 100(.965)^6 = 80.75 is left after 6 hours
Is this correct?
looks good
thank you
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Yes, your equation is correct. The exponential decay function that describes the quantity of a radioactive substance is formulated as y = a(1 - r)^t, where y represents the final quantity, a represents the initial quantity (in this case, 100), r represents the decay rate (in this case, 3.5% or 0.035), and t represents the time in hours.
So, substituting the given values, the equation becomes:
y = 100(1 - 0.035)^t
For 6 hours, we can substitute t = 6 into the equation and calculate the quantity remaining:
y = 100(1 - 0.035)^6
y ≈ 100(0.965)^6
y ≈ 100(0.83962)
y ≈ 83.962
Rounded to the nearest hundredth, 83.96 is left after 6 hours, which is the correct answer.