he number of bacteria in a culture is modeled by
n(t)=1710e071t
(a) The initial number of bacteria is
(b) The relative rate of growth of this bacterium population is
(c) The number of bacteria after 3 hours is
(d) After how many hours will the number of bacteria reach 10,000?
Your answer is
I got the A=1710
B=?
c=14389
D=?
I keep getting b and d wrong any suggestions. thanks in advance!
See your 5-12-12, 5:20PM post.
To find the answers to parts (b) and (d), we need to understand the equation n(t) = 1710e^0.71t, where n(t) represents the number of bacteria at time t.
(a) The initial number of bacteria is found by substituting t = 0 into the equation n(t). So, n(0) = 1710e^(0.71 * 0) = 1710e^0 = 1710. Therefore, the initial number of bacteria is 1710.
(b) The relative rate of growth of the bacterium population can be determined by examining the exponent in the equation. In this case, the coefficient of t in the exponent is 0.71. Since the exponent is positive, we can infer that the population is increasing over time. The relative rate of growth is quantified by the coefficient itself, which means the relative rate of growth is 0.71.
(c) To determine the number of bacteria after 3 hours, we substitute t = 3 into the equation n(t). Therefore, n(3) = 1710e^(0.71 * 3) = 1710e^2.13 ≈ 14,389. So, after 3 hours, the number of bacteria is approximately 14,389.
(d) To find the time at which the number of bacteria reaches 10,000, we need to solve the equation n(t) = 10,000. We substitute n(t) with 10,000 in the equation and solve for t.
10,000 = 1710e^(0.71t)
To isolate the variable, we will divide both sides of the equation by 1710.
10,000 / 1710 = e^(0.71t)
After evaluating the left-hand side, we can use the logarithmic function to solve for t.
5.847953216374269 = 0.71t
Dividing by 0.71 will give us the value of t.
t ≈ 8.24
Round to the nearest hour, so after approximately 8 hours, the number of bacteria will reach 10,000.
Therefore, (a) = 1710, (b) = 0.71, (c) ≈ 14,389, and (d) ≈ 8 hours.