a researcher observes a sample of a nuclide. an exponential model estimates that the mass, in grams, of the…

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)

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)

Answer

Explanation:

Step1: Recall exponential - decay formula

The general form of an exponential - decay formula is $M = M_0(1 - r)^t$, where $M_0$ is the initial mass, $r$ is the rate of decay, and $t$ is the time. Here, the initial mass $M_0 = 100$ grams and the rate of decay $r=0.24$ (since it decreases by 24% each minute), and $t$ is the number of minutes.

Step2: Substitute values into the formula

Substituting $M_0 = 100$, $r = 0.24$ into the formula $M = M_0(1 - r)^t$, we get $M=100(1 - 0.24)^t=100(0.76)^t$.

Answer:

c. $M = 100(0.76)^t$