The number of bacteria in a certain culture increased from 500 to 1000 between 7:00 A.M. and 9:00 A.M. Assuming growth is exponential, the number f(t) of bacteria t hours after 7:00 A.M. is given by f(t) = 500(2)^t/2.

(a) Estimate the number of bacteria in the culture at 8:00 A.M., 10:00 A.M., and 11:00 A.M. (Round your answers to the nearest whole number.)
8:00 A.M. bacteria
10:00 A.M. bacteria
11:00 A.M. bacteria

t = 1, t = 3 and t = 4

plug and chug
eg
for t = 1 (which is 8am)
500 * 2^(1/2)
500 * 1.414 = 707

To estimate the number of bacteria in the culture at different times, we need to use the formula provided: f(t) = 500(2)^(t/2), where f(t) is the number of bacteria t hours after 7:00 A.M.

To estimate the number of bacteria at 8:00 A.M., we need to calculate f(t) for t=1.
f(1) = 500(2)^(1/2)
= 500 * 1.4142 (rounded to four decimal places)
≈ 707.1
Therefore, at 8:00 A.M., there would be approximately 707 bacteria.

To estimate the number of bacteria at 10:00 A.M., we need to calculate f(t) for t=3.
f(3) = 500(2)^(3/2)
= 500 * 2.8284 (rounded to four decimal places)
≈ 1414.2
Therefore, at 10:00 A.M., there would be approximately 1414 bacteria.

To estimate the number of bacteria at 11:00 A.M., we need to calculate f(t) for t=4.
f(4) = 500(2)^(4/2)
= 500 * 4 (rounded to four decimal places)
= 2000
Therefore, at 11:00 A.M., there would be exactly 2000 bacteria.

In summary:
8:00 A.M. ≈ 707 bacteria
10:00 A.M. ≈ 1414 bacteria
11:00 A.M. = 2000 bacteria