Question

desmond is a scientist working with a culture of bacteria. 2500 bacteria in a petri dish are growing at a rate of 3% per second. which expression represents the number of bacteria in the petri dish after t seconds? p = 2500 · (1.03)^t p = 2500e^{0.03t} p = 2500e^{1.03t} p = 2500^{0.03t}

Explanation:

Step1: Recall growth - formula

The formula for exponential growth is \(p = p_0(1 + r)^t\), where \(p_0\) is the initial amount, \(r\) is the growth rate as a decimal, and \(t\) is the time.
Given \(p_0=2500\) and \(r = 0.03\).

Step2: Substitute values

Substitute \(p_0 = 2500\) and \(r=0.03\) into the formula \(p = p_0(1 + r)^t\), we get \(p = 2500\times(1 + 0.03)^t=2500\times(1.03)^t\).

Answer:

\(p = 2500\times(1.03)^t\) (the first option)