Question

in a lab experiment, 770 bacteria are placed in a petri dish. the conditions are such that the number of bacteria is able to double every 28 hours. how many bacteria would there be after 23 hours, to the nearest whole number?

Explanation:

Step1: Recall the exponential growth formula

The formula for exponential growth is \( N(t) = N_0 \times 2^{\frac{t}{T}} \), where \( N_0 \) is the initial number of bacteria, \( t \) is the time elapsed, \( T \) is the time it takes for the population to double, and \( N(t) \) is the number of bacteria at time \( t \).
Here, \( N_0 = 770 \), \( t = 23 \) hours, and \( T = 28 \) hours.

Step2: Substitute the values into the formula

Substitute the given values into the formula: \( N(23)=770\times2^{\frac{23}{28}} \)

First, calculate the exponent \( \frac{23}{28}\approx0.8214 \)

Then, calculate \( 2^{0.8214}\approx1.757 \) (using a calculator to find the value of the exponential term)

Step3: Calculate the final number of bacteria

Multiply the initial number of bacteria by the exponential term: \( N(23)=770\times1.757 \approx 1353 \)

Answer:

1353