A bacteria population is 3000 at time
t = 0
and its rate of growth is
1000 · 6t
bacteria per hour after t hours. What is the population after one hour? (Round your answer to the nearest whole number.)
To find the population after one hour, we need to substitute t = 1 into the growth equation and calculate the result.
Given:
Initial population (t = 0) = 3000
Rate of growth = 1000 · 6t
Substituting t = 1:
Rate of growth = 1000 · 6(1) = 1000 · 6 = 6000
To find the population after one hour, we need to add the rate of growth to the initial population:
Population after one hour = Initial population + Rate of growth
Population after one hour = 3000 + 6000 = 9000
Therefore, the population after one hour is 9000 (rounded to the nearest whole number).
To find the population after one hour, we need to substitute t = 1 into the growth function and calculate the result.
The growth function is given as 1000 · 6t bacteria per hour after t hours. So when t = 1, the growth rate is 1000 · 6(1) = 6000 bacteria per hour.
To find the population after one hour, we add the growth rate to the initial population:
3000 + 6000 = 9000 bacteria.
Therefore, the population after one hour is 9000 bacteria.
dp/dt = 6000 t
p = 3000 t^2 + c
at t = 0, p = c = 3000
p = 3000 t^2 + 3000
p at t = 1 = 3000+3000 = 6000