Question

A scientist counts the initial amount of bacteria in a petri dish to be 250. The bacteria growth rate doubles every 45 minutes. Part A: Determine an exponential equation based on the given information. Part B: Determine how many minutes (to the nearest tenth) it would take for the bacteria count to reach 1300.

Answer 1

Part A: The exponential equation that models the bacteria growth is N(t) = 250 * 2^(t/45) where N(t) is the number of bacteria after t minutes.

Part B: To find out how many minutes it would take for the bacteria count to reach 1300, we can solve the equation 1300 = 250 * 2^(t/45) for t. Taking the natural logarithm of both sides, we get ln(1300) = ln(250 * 2^(t/45)). Using the properties of logarithms, we can simplify this to ln(1300) = ln(250) + (t/45)*ln(2). Solving for t, we get t = (45 * (ln(1300) - ln(250))) / ln(2). Plugging in the values, we find that it would take approximately 97.8 minutes for the bacteria count to reach 1300.

Explanation: