# math

The number of bacteria in a petri dish doubles every 4 hours. If there are initially 200 bacteria.

a) How many bacteria will there be after 12 hours?

b) How many bacteria will there be after 2 days?

1. 👍
2. 👎
3. 👁
4. ℹ️
5. 🚩
1. y = A bᵗ

The starting amount of bacteria is 100, so A = 100

To find b, plug in this equation, t = 4 = and y = 200 (since the population doubles in 4 hours)

200 = 100 ∙ b⁴

Divide both sides by 2

200 / 100 = b⁴

b⁴ = 2

b = ∜2

y = A bᵗ

y = 100 ∙ (∜2 )ᵗ

a)

After 12 h:

y = 100 ∙ (∜2 )¹²

Since (∜2 )¹² = 2³

100 ∙ 2³ = 100 ∙ 8 = 800

b)

2 days = 48 h

y = 100 ∙ (∜2 )⁴⁸

Since (∜2 )⁴⁸ = 2¹²

y = 100 ∙ 2¹² = 100 ∙ 4096 = 409 600

1. 👍
2. 👎
3. ℹ️
4. 🚩
2. The previous post is wrong because I took the wrong starting value of the bacteria.

The solution should be written as follows:

y = A bᵗ

The starting amount of bacteria is 200, so A = 200

To find b, plug in this equation, t = 4 = and y = 400 (since the population doubles in 4 hours)

y = A bᵗ

y = 100 bᵗ

400 = 100 ∙ b⁴

Divide both sides by 4

400 / 100 = b⁴

b⁴ = 4

b = ∜4

b = √2

y = A bᵗ

y = 100 ∙ √2ᵗ

a)

After 12 h:

y = 100 ∙ ( √2 )¹²

Since ( √2 )¹² = 2⁶

100 ∙ 2⁶ = 100 ∙ 64 = 6 400

b)

2 days = 48 h

y = 100 ∙ ( √2 )⁴⁸

Since ( √2 )⁴⁸ = 2²⁴

y = 100 ∙ 2²⁴ = 100 ∙ 16 777 216 = 1 677 721 600

Ignore my first post.

1. 👍
2. 👎
3. ℹ️
4. 🚩

## Similar Questions

1. ### Calc

The number of bacteria in a culture is increasing according to the law of exponential growth. There are 125 bacteria in the culture after 2 hours and 350 bacteria after 4 hours. a) Find the initial population. b) Write an

2. ### Math

A certain type of bacteria is growing at an exponential rate that can be modeled by the equation y=ae^kt, where t represents the number of hours. There are 300 bacteria initially, and 1500 bacteria 5 hours later. How many bacteria

3. ### math

A Petri dish containing 500,000 bacteria is used in an experiment investigating growth rates for bacteria. The table below shows the number of bacteria, N(t), in the Petri dish after t minutes. t N(t) 1 520,000 2 540,800 3 562,432

4. ### Urgent math

The initial size of a culture of bacteria is 1000. After one hour the bacteria count is 4000. (a) Find a function n(t) = n0ert that models the population after t hours. n(t) = b)Find the population after 1.5 hours. (Round your

1. ### Honors Algebra

A biologist is researching a newly discovered species of bacteria. At time t=0 hours, she puts on hundred bacteria into a Petri dish. Six hours later, she measures 450 bacteria. Assuming exponential growth, what is the growth rate

2. ### calculus

2. The rate of change in the number of bacteria in a culture is proportional to the number present. In a certain laboratory experiment, a culture has 10,000 bacterial initially, 20,000 bacteria at time t1 minutes, and 100,000

3. ### Pre-Calc (exponential growth)

A COLONY OF BACTERIA IS GROWN UNDER IDEAL CONDITIONS IN A LAB SO THAT THE POPULATION INCREASES EXPONENTIALLY WITH TIME. At the end of the three hours, there are 10,000 bacteria. At the end of the 5 hours, there are 40,000

4. ### PreCalc

The initial size of a culture of bacteria is 1500. After 1 hour the bacteria count is 12000. (a) Find a function n(t) = n0e^rt that models the population after t hours. (Round your r value to five decimal places.) n(t) = (b) Find

1. ### algebra

bacteria can multiply at an increasing rate. The bacteria doubles every hour, how many bacteria will we have by the end of one 12 hours ?

2. ### Math

How do I solve this if there is no equation to this 1. The population of the bacteria in a Petri dish increases by a factor of 10 every 10 hour. If there are initally 20 bacteria in the dish, how long will it take before the