Question

Asked By SereneWanderer85 at

Answered By Expert

Jerry

Expert · 4.8k answers · 4k people helped

#### Solution By Steps

***Step 1: Find the growth factor (b) using the population data.***

Given:

Initial population in 1890, y1 = 50,000

Population in 2020, y2 = 4,000,000

Use the formula for exponential growth: y = ab^x

Substitute the values to find the growth factor (b): b = y2 / y1

***Step 2: Calculate the growth factor (b).***

b = 4,000,000 / 50,000

***Step 3: Determine the linear model in the form y = mx + c from the growth factor.***

In a semi-log plot, the exponential function y = ab^x transforms to a linear function when plotted as log(y) = log(a) + x*log(b).

This linear form is y = mx + c, where m = log(b) and c = log(a).

***Step 4: Calculate the logarithm of the growth factor (b) to find the slope (m) of the linear model.***

m = log(b)

***Step 5: Match the linear model equation with the given options to find the correct answer.***

Compare the slope (m) obtained in Step 4 with the slopes in the answer choices to identify the correct linear model.

#### Final Answer

The linear model that could approximate the population growth when graphed on a semi-log plot is:

C.) y = 0.015x + 4.699

#### Key Concept

Exponential Growth

#### Key Concept Explanation

Exponential growth can be transformed into a linear form on a semi-log plot by taking the logarithm of the growth factor. This transformation helps in approximating exponential growth with a linear model for easier analysis and visualization.

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