Question

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

Answer 1

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

Further explanation

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.

$\boxed{T_n = a + (n-1)d}$

$\boxed{S_n = \frac{1}{2}n ( 2a + (n-1)d )}$

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.

$\boxed{T_n = a ~ r^{n-1}}$

$\boxed{S_n = \frac{a( 1 - r^n ) }{1 - r}}$

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 = $1000 \times 2^{\frac{x}{5}}$

Population = y = $1000 \times (2^{\frac{1}{5}})^x$

Population = y = $\large{ \boxed {1000 \times (1.15)^x} }$

Let's prove the equation above :

After 5 hours :

Population = y = $1000 \times (1.15)^5$ = 2011 ≈ 2000 ✔

After 10 hours :

Population = y = $1000 \times (1.15)^{10}$ = 4046 ≈ 4000 ✔

After 15 hours :

Population = y = $1000 \times (1.15)^{15}$ = 8137 ≈ 8000 ✔

Learn more

• Geometric Series : brainly.com/question/4520950
• Arithmetic Progression : brainly.com/question/2966265
• Geometric Sequence : brainly.com/question/2166405

Answer details

Grade: Middle School

Subject: Mathematics

Chapter: Arithmetic and Geometric Series

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

Answer 2

Answer:

y = 1000(1.15)x

Step-by-step explanation:

Look at their's ^^^^