A major scientific periodical published an article in 1990...

A major scientific periodical published an article in 1990 dealing with the problem of global warming. The article was accompanied by a graph that illustrated two possible scenarios. (a) The warming might be modeled by an exponential function of the form $$ y=\left(1.046 \times 10^{-38}\right)\left(1.0444^{x}\right) $$ (b) The warming might be modeled by a linear function of the form $$ y=0.009 x-17.67 $$ In both cases, $x$ represents the year, and y represents the increase in degrees Celsius due to the warming. Use these functions to approximate the increase in temperature for each of the following years. $$ 2040 $$

A major scientific periodical published an article in 1990 dealing with the problem of global warming. The article was accompanied by a graph that illustrated two possible scenarios.
(a) The warming might be modeled by an exponential function of the form
$$
y=\left(1.046 \times 10^{-38}\right)\left(1.0444^{x}\right)
$$
(b) The warming might be modeled by a linear function of the form
$$
y=0.009 x-17.67
$$
In both cases, $x$ represents the year, and y represents the increase in degrees Celsius due to the warming. Use these functions to approximate the increase in temperature for each of the following years.
$$
2040
$$

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Key Concepts

Function Evaluation

Function evaluation involves substituting a specific value for the independent variable into a given mathematical function to compute the corresponding value of the dependent variable. This process is essential for making predictions based on mathematical models.

Mathematical Modeling of Global Warming

Mathematical modeling of global warming uses functions to approximate changes in temperature over time. These models, whether linear or exponential, help scientists predict future temperature trends based on past and current data, thereby providing insights into potential environmental impacts.

Exponential Functions

Exponential functions describe phenomena where the rate of change of a quantity is proportional to its current value. They are useful for modeling processes that involve rapid growth or decay, where small changes in the independent variable can lead to significant changes in the outcome over time.

Linear Functions

Linear functions represent relationships with a constant rate of change, meaning the relationship between the variables is proportional. They are often used to model situations where changes occur at a steady rate, making them straightforward for predictions over time.

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