Question

each figure has the same data points. however, each figure has a different curve fitting the data. the equation for each curve is also shown. answer the questions that follow. figure 1 figure 2 figure 3 y = 200(0.93)^x + 50 y = 504(0.98)^x y = - 0.26x + 380 (a) which curve fits the data best? figure 1 figure 2 figure 3 (b) use the equation of the best fitting curve from part (a) to predict the amount of the radioactive substance after 80 days. round your answer to the nearest hundredth. milligrams

Explanation:

Step1: Visual inspection

By looking at the three figures, the curve in Figure 2 seems to pass closer to more data - points compared to the curves in Figure 1 and Figure 3. So the best - fitting curve is the one in Figure 2.

Step2: Substitute value into equation

The equation of the curve in Figure 2 is $y = 504(0.98)^{x}$. We want to find the value of $y$ when $x = 80$. Substitute $x = 80$ into the equation: $y=504\times(0.98)^{80}$.

Step3: Calculate the result

First, calculate $(0.98)^{80}$. Using a calculator, $(0.98)^{80}\approx0.20067$. Then, $y = 504\times0.20067\approx101.14$.

Answer:

(a) Figure 2
(b) 101.14