A bacteria culture initially contains 100 cells and grows at a rate proportional to its size. After an hour the population has increased to 570. (a) Find an expression for the number of bacteria after t hours. P(t) = (b) Find the number of bacteria after 4 hours. (Round your answer to the nearest whole number.) P(4) = bacteria (c) Find the rate of growth after 4 hours. (Round your answer to the nearest whole number.) P'(4) = bacteria per hour (d) When will the population reach 10,000? (Round your answer to one decimal place.)

Step-by-step explanation:

In one hour, the population has increased from 100 to 570.

The population becomes  % of 100.

Hence, according to our observation, we can tell that the population of the bacteria grows up to 570%  of previous hour.

(a)

The number of bacteria after t hours can be represented as .

(b)

After 4 hours, the number of bacteria will be .

(c)

The derivative of p(t) is .

At t = 4, the value will be 183723.6268 ≅ 183724.

(d)

The population will be 10,000 that is p(t) = 10000.

.

constant acceleration- a

constant velocity- c

no velocity or acceleration- b

explanation:

for body moving with a constant acceleration, the rate of change of displacement changes over time. this is proven by the increasing gradient of the curve (a) against time.

a body that is moving at constant velocity covers equal distances over equal periods of time, thus the straight line with a constant gradient c.

a stationary body   covers no displacement as time elapses. thus the flat line with   zero gradient.