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 Application equation to model this situation. What are the slope and y-intercept? Explain. Hint:

## The correct answer is: 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.

### 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 = 1,500The 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.  #### With Turito Foundation. #### Get an Expert Advice From Turito.  