Question

a researcher observes a sample of a nuclide. an exponential model estimates that the mass, in grams, of the sample decreases by 24% every 22.96 minutes. which of the following equations could represent this model, where m is the estimated mass, in grams, of the sample t minutes after the researcher began observing the sample? a. m = 100(0.24)^(t/22.96) b. m = 100(0.24)^(t+22.96) c. m = 100(0.76)^(t+22.96) d. m = 100(0.76)^(t/22.96)

Explanation:

Step1: Identify decay - formula

The general formula for exponential decay is $M = M_0(1 - r)^{\frac{t}{h}}$, where $M_0$ is the initial mass, $r$ is the decay rate, $t$ is the time elapsed, and $h$ is the time - interval for the given decay rate. Here, the mass decreases by 24% every 22.96 minutes. So $r=0.24$ and $h = 22.96$.

Step2: Write the decay equation

If we assume the initial mass is $M_0 = 100$ (for simplicity of showing the proportion), the mass $M$ at time $t$ minutes is given by $M = 100(1 - 0.24)^{\frac{t}{22.96}}=100(0.76)^{\frac{t}{22.96}}$.

Answer:

d. $M = 100(0.76)^{\frac{t}{22.96}}$