Question

The graph shows the population y of a bacterial colony after x minutes.

Identify and interpret the y-intercept.

Write an exponential function that represents the population.

Then estimate the population after 10 minutes. Round your answer to the nearest whole number.

The y-intercept is ____
This is the number of bacteria at time x= ___
An exponential function that represents the population is y= __ ⋅ (__)^x
The population after 10 minutes is ____

Answer 1

The exponential function that represents the population is y = 200(1.5)ˣ

Exponential function

An exponential function is given by:

y = abˣ

Let y, x are variables, a is the initial value and b is the multiplication factor.

Where y is the population of the bacteria after x minutes.

From the graph, at the point:

(0, 200):

200 = ab⁰

a = 200

at the point (2, 450):

450 = 200(b²)

b = 1.5

The exponential function that represents the population is y = 200(1.5)ˣ

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