Question

suppose a culture of bacteria begins with 5000 cells and dies by 30% each year. write an equation that represents this situation. y=5000(0.7)^x y=5000(0.3)^x y=5000(1.3)^x y=30(5000)^x

Explanation:

Step1: Identify decay formula

The general formula for exponential decay is \( y = a(1 - r)^x \), where \( a \) is the initial amount, \( r \) is the rate of decay, and \( x \) is time.

Step2: Substitute values

Here, \( a = 5000 \), \( r = 0.30 \) (30% decay). So \( 1 - r = 1 - 0.30 = 0.70 \). Substituting into the formula gives \( y = 5000(0.7)^x \).

Answer:

\( y = 5000(0.7)^x \) (corresponding to the first option: \( y = 5000(0.7)^x \))