Una población de bacterias crece de tal manera que la razón de crecimiento en el instante t (medido en horas) es igual a p'(t) = 90t + 500 / 1 + t

Si el tamaño de la población inicial es de 2000 bacterias. Encontrar el tamaño de la población al cabo de 3 horas.

By the fundamental theorem of calculus, if

p'(t) = 90t + 500/(1 + t)

and p(0) = 2000, then

p(t) = p(0) + ∫₀ᵗ p'(u) du

⇒   p(t) = 2000 + ∫₀ᵗ (90u + 500/(1 + u)) du

⇒   p(t) = 2000 + (45u² + 500 ln|1 + u|)₀ᵗ

⇒   p(t) = 2000 + 45t² + 500 ln|1 + t|

Then after t = 3 hours, the population of bacteria would be

p(3) = 2000 + 45•3² + 500 ln(1 + 3) ≈ 3098

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

eventually after a few more steps, your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x

for a it would be 24 children.

for b i don't understand the question. is it saying for each individual person they pick 5 reds to 7 greens or is it the whole group. clarify and i hope this can you.

step-by-step explanation: