IDNLearn.com is designed to help you find the answers you need quickly and easily. Find the information you need quickly and easily with our reliable and thorough Q&A platform.
Sagot :
The completed statement is as follows;
The model of the data is; [tex]\underline{P \approx 3.6 \cdot e^{-2.35 \times 10^{-2} \times t}}[/tex]. The exponential model
suggest that the honeybees colonies have an approximately -2.35 percent
growth rate per year. If this trend continues, the number of honeybee
colonies 40 years after 1989 will be around 1.40625 million. Given that the
correlation coefficient indicates a correlation between the model and the
data, predictions made by the model is approximately correct.
Reasons:
The table of values is presented as follows;
[tex]\begin{tabular}{|c|c|}\underline{Years since 1989} &\underline{Honeybee Colonies (millions)}\\0&3.6\\4&3.1\\8&2.8\\12&2.65\\16&2.6\\20&2.25\end{array}\right][/tex]
The general form of an exponential growth function is; [tex]P = \mathbf{P_0 \cdot e^{k \cdot t}}[/tex]
When t = 0, we have;
[tex]P = P_0 \cdot e^{k \times 0} = 3.6[/tex]
Therefore;
P₀ = 3.6
When t = 20, we have;
[tex]P = 3.6 \cdot e^{k \times 20} = 2.25[/tex]
Solving gives;
k ≈ -2.35 × 10⁻²
The exponential model is therefore;
[tex]\underline{P \approx 3.6 \cdot e^{-2.35 \times 10^{-2} \times t}}[/tex]
The exponential model suggest that the honeybees colonies have an
approximately -2.35 percent growth rate.
After 40 years, we have;
[tex]P \approx 3.6 \cdot e^{-2.35 \times 10^{-2} \times 40} \approx 1.40625[/tex]
If the trend continues, the number of honeybee colonies 40 years after 1989 will be approximately 1.40625 million
Expressing the growth rate as a logarithm, we have;
ln(P) = ln(3.6) - 2.35×10⁻²·t
The correlation between the values is found as follows;
[tex]\displaystyle r_p = \mathbf{\frac{\sum y_1 \cdot y_2}{\sqrt{\sum y_1^2 \cdot \sum y_2^2} }} \approx 0.99939[/tex]
Where;
y₁ = The logarithm of the measured correlation.
Therefore, because the correlation coefficient indicates a correlation
between the model and the data, predictions made by this model is
approximately correct.
Learn more about exponential model here:
https://brainly.com/question/16873037
Thank you for contributing to our discussion. Don't forget to check back for new answers. Keep asking, answering, and sharing useful information. For precise answers, trust IDNLearn.com. Thank you for visiting, and we look forward to helping you again soon.
