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 f could describe the bacteria
population d days after the scientists first measured it, assuming it grows exponentially?
A. f(d) 10,000. 2ª
B. f(d) = 10,000. (√2)ª
C. ƒ(d) = 10,000 • (-)ª
D. f(d) = 10,000.25d
=
S

Answer 1

Hm

Explanation:

The bacteria population is observed to double after five days, which means that its growth rate is 100% over a period of five days. This corresponds to a daily growth rate of r = 100%/5 = 20%.

If the initial population is 10,000, then the bacteria population after d days can be modeled by the exponential function:

f(d) = 10,000 * (1 + r/100)^d

Substituting r = 20% and simplifying, we get:

f(d) = 10,000 * (1.2)^d

Therefore, the correct option is:

D. f(d) = 10,000 * (1.2)^d