Maths-

General

Easy

Question

# A certain population of bacteria had an initial population of 1500. It then started growing at a rate of 2000 per day. Write the equation to model this situation. What are the slope and y-intercept? Explain.

## The correct answer is: 1,500

### Hint:-

1. Growth in population of bacteria = Number of days of growth * rate of growth per day

2. Total population of bacteria = y = Initial population + Growth in population.

3. The slope of a line can be defined as the change in y coordinates of any 2 points on that line corresponding to the change in the x coordinates of those 2 points. This is generally referred to as the rise to run ratio of the given line i.e. how much did the y-coordinates rise vis-a-vis how long a distance was covered by the x-coordinates.

4. y-intercept for any line refers to the point at which the given line intersects with the Y-axis. At this point the x-coordinate is 0.

Step-by-step solution:-

Let the number of days for which the population of bacteria is observed to grow be x days and the total population of bacteria be y.

Now,

Growth in population of bacteria = Number of days of growth * rate of growth per day

∴ Growth in population of bacteria = x * 2,000 per day .......................................................................... (From given information)

∴ Growth in population of bacteria = 2,000 x ........................................................................................... (Equation i)

Now, we know that-

Total population of bacteria = y = Initial population + Growth in population.

∴ Total population of bacteria = y = 1,500 + 2,000 x .......................................................... (From given information & Equation i)

i.e. y = 2,000 x + 1,500 ................................................................................................................................. (Equation ii)

Comparing Equation ii with slope intercept form of a line i.e. y = mx + b, we get-

Slope = m = 2,000

& Y-intercept = b = 1,500

The slope of a line can be defined as the change in y coordinates of any 2 points on that line corresponding to the change in the x coordinates of those 2 points. This is generally referred to as the rise to run ratio of the given line i.e. how much did the y-coordinates rise vis-a-vis how long a distance was covered by the x-coordinates.

In the given situation, slope of the given equation refers to the movement in population of bacteria for every increase in the days that it is continues to grow.

since the slope = 2,000, we can say that for every day that the bacteria continues to grow, its population count increases by 2,000.

Also, y-intercept for any line refers to the point at which the given line intersects with the Y-axis.

At this point the x-coordinate is 0.

This means that when the value of x-coordinate is 0, the value of y-coordinate is 1,500.

For the given situation, this means that the population of bacteria, at the start i.e. befor any growth happened, will be 1,500.

Final Answer:-

∴ The given line can be written as- y = 2,000 x + 1,500. Its slope (i.e. change in population for a given change in time period) is 2,000. Its Y-intercept (i.e. population at 0 days or before starting growth) is 1,500.

### Related Questions to study

Maths-

### The ratio of base to the height of a triangle is 16: 10 and its area is 80 m². Find the height and base of such a triangle.

### The ratio of base to the height of a triangle is 16: 10 and its area is 80 m². Find the height and base of such a triangle.

Maths-General

Maths-

### If the perimeter of an equilateral triangle is 420 units. find half of its area.

### If the perimeter of an equilateral triangle is 420 units. find half of its area.

Maths-General

Maths-

### The base of a triangle is four times its height. What is the area of the triangle?

### The base of a triangle is four times its height. What is the area of the triangle?

Maths-General

Maths-

### If the perimeter of an equilateral triangle is 342 units. Then find its area.

### If the perimeter of an equilateral triangle is 342 units. Then find its area.

Maths-General

Maths-

### A star is made up of 4 equilateral triangles and a square. If the sides of the triangles are 8 units, what is the surface area of the star ?

### A star is made up of 4 equilateral triangles and a square. If the sides of the triangles are 8 units, what is the surface area of the star ?

Maths-General

Maths-

### If the side AC of a given triangle is 18 units and the height of the triangle is 10 units, what is the area of triangle ABC ?

### If the side AC of a given triangle is 18 units and the height of the triangle is 10 units, what is the area of triangle ABC ?

Maths-General

Maths-

### A triangle has an area of 90 𝑚^{2} and a base of 12 m, find the height of such a triangle?

### A triangle has an area of 90 𝑚^{2} and a base of 12 m, find the height of such a triangle?

Maths-General

Maths-

### If the height to base ratio of a triangle ABC is 3:4 and the area is 864 square units. Determine the height and base of this triangle.

### If the height to base ratio of a triangle ABC is 3:4 and the area is 864 square units. Determine the height and base of this triangle.

Maths-General

Maths-

### If the side of an equilateral triangular park is 20 units. What will be half of its area ?

### If the side of an equilateral triangular park is 20 units. What will be half of its area ?

Maths-General

Maths-

### If the base of a triangle becomes three times its height. What is the new area of a triangle?

### If the base of a triangle becomes three times its height. What is the new area of a triangle?

Maths-General

Maths-

### The side of an equilateral triangle is 16 units. What will be the double of its area ?

### The side of an equilateral triangle is 16 units. What will be the double of its area ?

Maths-General

Maths-

### In triangle ABC, AB = 8cm. If the altitudes corresponding to AB and BC are 4 cm and 5 cm respectively. Find the measure of BC.

### In triangle ABC, AB = 8cm. If the altitudes corresponding to AB and BC are 4 cm and 5 cm respectively. Find the measure of BC.

Maths-General

Maths-

### The base and corresponding altitude of a parallelogram are 18 cm and 6 cm respectively. Find its area

### The base and corresponding altitude of a parallelogram are 18 cm and 6 cm respectively. Find its area

Maths-General

Maths-

### The ratio of the bases of two triangles is a : b. If the ratio of their corresponding altitudes is c : d, find the ratio of their areas (in the same order).

### The ratio of the bases of two triangles is a : b. If the ratio of their corresponding altitudes is c : d, find the ratio of their areas (in the same order).

Maths-General

Maths-

### The sides of triangle are 11 cm, 15 cm and 16 cm. What is the measure of altitude to the largest side?

### The sides of triangle are 11 cm, 15 cm and 16 cm. What is the measure of altitude to the largest side?

Maths-General