Question

as part of a biology experiment, priscilla observes the growth of mold on a piece of bread. at the start, \\(\frac{1}{10}\\) of the surface is covered with mold. she determines the mold is growing at a rate of 24% per day. which equation represents the percentage of the bread surface covered in mold, \\(p\\), given the amount of time in days, \\(t\\)? \\(\bigcirc\\) a. \\(p = 0.1(0.24)^t\\) \\(\bigcirc\\) b. \\(p = 0.1(1.24)^t\\) \\(\bigcirc\\) c. \\(p = 0.24(0.1)^t\\) \\(\bigcirc\\) d. \\(p = 0.24(1.1)^t\\)

Explanation:

Step1: Recall exponential growth formula

The general formula for exponential growth is \( p = a(1 + r)^t \), where \( a \) is the initial amount, \( r \) is the growth rate (in decimal), and \( t \) is time.

Step2: Determine initial amount \( a \)

The initial fraction of the surface covered is \( \frac{1}{10}=0.1 \), so \( a = 0.1 \).

Step3: Determine growth rate \( r \)

The growth rate is \( 24\% = 0.24 \), so \( 1 + r = 1 + 0.24 = 1.24 \).

Step4: Form the equation

Substituting \( a = 0.1 \) and \( 1 + r = 1.24 \) into the exponential growth formula, we get \( p = 0.1(1.24)^t \).

Answer:

B. \( p = 0.1(1.24)^t \)