Question

Growth of Bacteria in a Culture Suppose the rate of growth of bacteria in a Petri dish is given by q(t) = 3^t, where t is given in hours and q(t) is given in thousands of bacteria per hour. If a culture starts with 10,000 bacteria, find a function Q(t) that gives the number of bacteria in the Petri dish at any time t. How many bacteria are in the dish after 2 hours? Solution We have Q(t) = ? 3^t dt = 3^t / ln 3 + C. Then, at t = 0 we have Q(0) = 10 = 1 / ln 3 + C, so C ? 9.090 and we get Q(t) = 3^t / ln 3 + 9.090. At time t = 2, we have Q(2) = 3^2 / ln 3 + 9.090 = 17.282. After 2 hours, there are 17,282 bacteria in the dish. 1.35 From Example 1.42, suppose the bacteria grow at a rate of q(t) = 2^t. Assume the culture still starts with 10,000 bacteria. Find Q(t). How many bacteria are in the dish after 3 hours?

          Growth of Bacteria in a Culture

Suppose the rate of growth of bacteria in a Petri dish is given by q(t) = 3^t, where t is given in hours and q(t) is given in thousands of bacteria per hour. If a culture starts with 10,000 bacteria, find a function Q(t) that gives the number of bacteria in the Petri dish at any time t. How many bacteria are in the dish after 2 hours?

Solution
We have
Q(t) = ? 3^t dt = 3^t / ln 3 + C.
Then, at t = 0 we have Q(0) = 10 = 1 / ln 3 + C, so C ? 9.090 and we get
Q(t) = 3^t / ln 3 + 9.090.
At time t = 2, we have
Q(2) = 3^2 / ln 3 + 9.090
= 17.282.
After 2 hours, there are 17,282 bacteria in the dish.

1.35 From Example 1.42, suppose the bacteria grow at a rate of q(t) = 2^t. Assume the culture still starts with 10,000 bacteria. Find Q(t). How many bacteria are in the dish after 3 hours?

Growth of Bacteria in a Culture

Suppose the rate of growth of bacteria in a Petri dish is given by q(t) = 3^t, where t is given in hours and q(t) is given in thousands of bacteria per hour. If a culture starts with 10,000 bacteria, find a function Q(t) that gives the number of bacteria in the Petri dish at any time t. How many bacteria are in the dish after 2 hours?

Solution
We have
Q(t) = ? 3^t dt = 3^t / ln 3 + C.
Then, at t = 0 we have Q(0) = 10 = 1 / ln 3 + C, so C ? 9.090 and we get
Q(t) = 3^t / ln 3 + 9.090.
At time t = 2, we have
Q(2) = 3^2 / ln 3 + 9.090
= 17.282.
After 2 hours, there are 17,282 bacteria in the dish.

1.35 From Example 1.42, suppose the bacteria grow at a rate of q(t) = 2^t. Assume the culture still starts with 10,000 bacteria. Find Q(t). How many bacteria are in the dish after 3 hours?

Added by Michael B.

Question

Please give Ace some feedback