Question

A bacteria culture is started with 300 bacteria. After 4 hours, the population has grown to 708 bacteria. If the population grows exponentially according to the formula Pt​=P₀​(1+r)ᵗ (a) Find the growth rate. Round your answer to the nearest tenth of a percent. (b) If this trend continues, how many bacteria will there be in one day? bacteria (c) How long will it take for this culture to triple in size? R

Answer 1

The growth rate of the bacteria culture is approximately 27.4%. If this trend continues, the estimated population after one day would be around 3,962,020 bacteria. Also, it will take about 9 hours for the bacterial culture to triple in size.

Step-by-step explanation:

To find the growth rate (r), use the given formula Pt=P₀​(1+r)ᵗ and plug in the given values. Here, P₀ represents the initial population (300), Pt represents the population after given time period (708) and t is the time period in hours (4). After solving, the growth rate comes out to be around 27.4% or 0.274 when represented as a decimal.

To find out the population after one day (24 hours), we'll use the same formula, but with the calculated growth rate and t = 24. So, P24 = 300(1 + 0.274)^24, which gives a value around 3,962,020 bacteria.

Lastly, for the bacteria culture to triple in size, we'll set Pt as 3 * 300 = 900 and solve for t. So, 900 = 300(1 + 0.274)^t. Solving gives t = 8.7 hours, or roughly 9 hours.

Learn more about Exponential Growth