Hurryyy a bacteria population doubles in size every 5 hours. after 5 hours, the sample contains 2,000 bacteria. which equation best models y, the population size after x hours? y = 1000(1.15)x y = 1000(2)x y = 1000(2.5)x y = 1000(3)x

Equation of y, the population size after x hours is y = 1000 (1.15)ˣ

Firstly , let us learn about types of sequence in mathematics.

Arithmetic Progression is a sequence of numbers in which each of adjacent numbers have a constant difference.

Tn = n-th term of the sequence

Sn = sum of the first n numbers of the sequence

a = the initial term of the sequence

d = common difference between adjacent numbers

Geometric Progression is a sequence of numbers in which each of adjacent numbers have a constant ration.

Tn = n-th term of the sequence

Sn = sum of the first n numbers of the sequence

a = the initial term of the sequence

r = common ratio between adjacent numbers

Let us now tackle the problem!

Let :

Initial number of population = a

After 5 hours → Population = y = a × 2 = 2000

2a = 2000

a = 2000 ÷ 2

a = 1000

After 10 hours → Population = y = a × 2 × 2 = a × 2² = 1000 × 2²

After 15 hours → Population = y = a × 2 × 2 × 2 = a × 2³ = 1000 × 2³

After x hours ↓

Population = y =

Population = y =

Population = y =

Let's prove the equation above :

After 5 hours :

Population = y = = 2011 ≈ 2000 ✔

After 10 hours :

Population = y = = 4046 ≈ 4000 ✔

After 15 hours :

Population = y = = 8137 ≈ 8000 ✔

Grade: Middle School

Subject: Mathematics

Chapter: Arithmetic and Geometric Series

Keywords: Arithmetic , Geometric , Series , Sequence , Difference , Term

85.560%

step-by-step explanation:

conditional probability is defined as:

p(a|b) = p(a∩b) / p(b)

in other words, the probability that a occurs, given that b has occurred = the probability that both a and b occur / the probability that b occurs.

in this example:

p(turns 64 | turns 44) = p(turns 64 & turns 44) / p(turns 44).

if someone turns 64, they must have already turned 44, so:

p(turns 64 | turns 44) = p(turns 64) / p(turns 44)

on page 42, we see that of the original 100,000, 94944 turn 44, and 81234 turn 64.   therefore:

p(turns 64 | turns 44) = 81234 / 94944

p(turns 64 | turns 44) = 0.85560