Math  /  Algebra

QuestionA 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 data might be modeled by an exponential function of the form f(x)=(1.045×1038)(1.0443x)f(x)=\left(1.045 \times 10^{-38}\right)\left(1.0443^{x}\right). (b) The warming might be modeled by a linear function of the form g(x)=0.009x17.66g(x)=0.009 x-17.66
In both cases, xx represents the year, and the function value represents the increase in degrees Celsius due to the warming. Use these functions to approximate the increase in temperature in 2002, to the nearest tenth. (a) According to the exponential model, what is the predicted increase in temperature in 2002?
The predicted increase in temperature in 2002 is about \square C{ }^{\circ} \mathrm{C}. (Round to the nearest tenth as needed.)

Studdy Solution
Calculate the result and round to the nearest tenth.
First, calculate 1.044312 1.0443^{12} .
Then multiply the result by 1.045×1038 1.045 \times 10^{-38} .
f(12)(1.045×1038)×(1.044312) f(12) \approx \left(1.045 \times 10^{-38}\right) \times (1.0443^{12})
After calculating, round the result to the nearest tenth.
The predicted increase in temperature in 2002 is approximately 0.0C \boxed{0.0} \, ^{\circ} \mathrm{C} .

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