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

i think the answer would be c

you estimate that the angle of elevation to the top of the 86th floor (the observatory) is 82 .the total height of the building is another 123 meters above the 86th floor.

leave feedback if u need : )