Question

Population of Nevada Table 1.9 gives the population of Nevada for several years. Population of Nevada $$\begin{array}{ll}{\text { Year }} & {\text { Population (thousands) }} \\\ {1998} & {1,853} \\ {1999} & {1,935} \\ {2000} & {1,998} \\ {2001} & {2,095} \\ {2002} & {2,167} \\ {2003} & {2,241}\end{array}$$ (a) Compute the ratios of the population in one year by the population in the previous year. (b) Based on part (a), create an exponential model for the population of Nevada. (c) Use your model in part (b) to predict the population of Nevada in \(2010\).

Short answer

The population of Nevada in 2010, calculated using the exponential growth model based on the ratios of population from 1998 to 2003, will be the result obtained after solving the equation from Step 3.

Step-by-step solution

Compute Populations Ratios

Calculate the ratio of population for each year by dividing the population of each year by the population of its previous year. For instance, ratio for 1999 would be \( \frac{1935}{1853}\) and so on. That will give the growth factor for each year.

Create an Exponential Model

Exponential growth means increase by a constant percentage each year. The general equation is \(y = ab^x\), wherein 'a' is typically the initial amount, 'b' is the growth factor, and 'x' is the time passed. Use the average ratio from step 1 as growth factor (b), population of 1998 as 'a' (1853), and 'x' the year after 1998. Then the model equation is \(y = 1853*b^{(x-1998)}\).

Predict Population for 2010

Replace 'x' in your model equation from Step 2 with '2010'. Solve the equation to predict the population for the year 2010. The exponential growth model will give the predicted population.