Question

Scientists measure a bacteria population and find that it is 10,000. Five days later, they find that the population has doubled. Which function ƒ could describe the bacteria population d days after the scientists first measured it, assuming it grows exponentially?

A. f(d) = 10,000.2d
B. f(d) = 10,000 (2)
C. f(d) = 10,000 (1) d 2
D. f(d) = 10,000.25d

Answer 1

The correct function to describe the exponential growth of the bacteria population is D. f(d) = 10,000 × 2^(d/5), which reflects the doubling of the population every five days starting with an initial population of 10,000.

Step-by-step explanation:

Let's examine the options to describe an exponential function representing the growth of a bacteria population. The student stated that the initial bacteria population was 10,000, and it doubled over a period of five days. To model exponential growth, we need an equation that reflects this doubling effect over a period of time.

The correct answer is D. f(d) = 10,000 × 2(d/5). This function uses the initial population (10,000) and shows that it doubles every five days, so the exponent is (d/5) where 'd' is the number of days after the initial measurement.

Option A, B. f(d) = 10,000 × 2(1), suggests a constant multiple, which is not representative of exponential growth. Option C, C. f(d) = 10,000 × (1) d × 2, and Option D, D. f(d) = 10,000 × .25d, do not accurately represent the described bacterial growth pattern.

Remember, exponential growth in populations like bacteria shows that the growth rate—the number of organisms added in each reproductive generation—is increasing at a greater and greater rate, leading to a J-shaped growth curve.