MATH SOLVE

6 months ago

Q:
# Dr. Steve is working with a new radioactive substance in his lab. He currently has 64 grams of the substance and knows that it decays at a rate of 25% every hour.Identify whether this situation represents exponential growth or decay. Then determine the rate of growth or decay, r, and identify the initial amount, A.

Accepted Solution

A:

Answer:3 hoursStep-by-step explanation:This situation represents exponential decay which decays 25% every hour.Rate of decay = r = 0.25Initial amount = A = 64Equation y = a (1 - r) ^ twhere y is final amount = 27g t is the time = to find27 = 64(1 - 0.25)^t27/64 = (1 - 0.25)^t0.42 = (1 - 0.25)^tTake log ln(0.42) = ln(1 - 0.25)^tln(0.42) = (t) ln(1 - 0.25)t = ln(0.42)/ln(1 - 0.25)t = 3.015 hourst ≈ 3 hours