PLEASE asnwers both Sure! Here's a transcription and detailed explanation of the image for educational purposes:---**Scenario Description:**A student needs to type a 50-page report and turn it in within 14 days. They recorded their progress over 10 days using the scatterplot below. They used a polynomial function \( p(d) \) to model the total number of pages, \( p \), typed after \( d \) days. They calculated the coefficient of determination to be 0.33.**Question:**Can they use this model to predict how many pages they will finish in 13 days?**Scatterplot Explanation:**- **X-axis (Horizontal):** Represents the number of days (\(d\)) ranging from 0 to 14.- **Y-axis (Vertical):** Represents the total number of pages typed (\(p\)) ranging from 0 to 50.- **Data Points:** Blue dots indicate the actual number of pages typed on each day.- **Polynomial Function:** The red curve represents a polynomial function \( p(d) = 0.34d^2 - 0.09d \) fitted to the data points.- **Coefficient of Determination (\(r^2\)):** Displayed as 0.33, indicating the model’s fit.**Response Options:**1. **Yes.** The model has a moderate fit, and they can safely extrapolate to \(d=13\).2. **No.** The model has a weak fit, and no predictions can be made. The student should consider using an exponential model instead.3. **No.** The model has a moderate fit, and \(d=13\) would be considered an extreme extrapolation value. The student should consider using a linear model instead.4. **Yes.** The model has a moderate fit, and they can use interpolation to predict what happens at \(d=13\).--- This explanation helps students understand model fitting and prediction within the context of progress tracking and data modeling using polynomial functions. **Transcription for Educational Website:**---**Balloon Height Prediction Analysis**A group of mathematicians recorded the height of an air balloon \( t \) minutes after ignition. The heights from 1 to 10 minutes are shown in the scatter plot below. They are interested in predicting the height after 15 minutes. They modeled their data with an exponential function and computed \( f(15) = 980.19 \). They concluded that the air balloon will be approximately 980 feet high after 15 minutes.*Can they trust this prediction?*### Mathematical ModelThe function used to model the data is:\[ f(t) = -900e^{-0.2t} + 1025 \]with \( r^2 = 0.82 \).### Graph and Data ExplanationThe scatter plot illustrates the height (in feet) against the time (in minutes). The blue dots represent the actual recorded data points, while the red curve is the exponential function fitting these points. The \( r^2 \) value of 0.82 suggests a decent fit, indicating that the model explains 82% of the variance in the data.### Prediction Evaluation OptionsConsider the following evaluation regarding the trustworthiness of the prediction:- \( \circ \) Yes, they can trust this prediction since \( f(15) = 980.19 \) and \( r^2 \) is close to 1.- \( \circ \) No, they cannot trust this prediction since \( f(15) = 985.21 \).- \( \circ \) No, they cannot trust this prediction since \( x = 15 \) is too far from the known data values.- \( \circ \) Yes, they can trust this prediction since the data follows an exponential trend.---

We have given coefficients of determination..means only 33% data is explained by this…

A student needs to type a 50-page report and turn it in within 14 days. They recorded their progress over 10 days using the scatterplot below. They used a polynomial function p(d) to model the total number of pages, p, typed after d days. They calculated the coefficient of determination to be 0.33. Can they use this model to predict how many pages they will finish in 13 days? Total Number of Pages 50 45 40 35 30 25 20 15 10 5 p(d) = 0.34d² -0.09d 7²=0.33 3 4 5 6 7 Days 8 9 Yes. The model has a moderate fit, and they can safely extrapolate to d=13. 10 11 12 13 14 No. The model has a weak fit, and no predictions can be made. The student should consider using an expo- nential model instead. No. The model has a moderate fit, and d=13 would be considered an extreme extrapolation value. The student should consider using a linear model instead. Yes. The model has a moderate fit, and they can use interpolation to predict what happens at d=13.