# College math – quadratic and exponential regression

**Please be confident to do BOTH the quadratic AND exponential retreat projects.**

**Quadratic Model**

**QR--****‐****4: Input Term of Day (hour) **14.5

**QR--****‐****6: Target Outdoor Latitude **53.0

**Exponential Model**

**ER--****‐****4: Input Gone-by Term (minutes) **102

**ER--****‐****5: Target Coffee Latitude **96

**Tasks for Quadratic Retreat Design (QR)**

**(QR-1)**Plot the points (*x*,*y*) to get a**scatterplot**. Note that the bear is definitely non-linear. Use an alienate lamina on the tame and upright axes and be confident to write carefully.

**(QR-2)**Find the**quadratic polynomial of best fit**and**graph**it on the scatterplot. Recite the**formula**for the quadratic polynomial.

**(QR-3)**Find and recite the esteem of**r**** ^{2}**, the coefficient of gratification. Discuss your discoverings. (

*r*

^{2}is adapted using a unanalogous formula than for rectirectirectistraight retreat. However, sound as in the rectirectirectistraight request, the closer

*r*

^{2}is to 1, the amend the fit.Just performance delay

**r****, not**

^{2}*r*.) Is a parabola a amiable flexion to fit to this postulates?

**(QR-4)**Use the quadratic polynomial to effect an outdoor latitude**estimate**. Each collocate portion accomplish calculate a latitude like for a unanalogous term of day assigned by your tutor. Be confident to use the quadratic retreat design to effect the like (not the esteems in the postulates board). Recite your results perspicuously -- the term of day and the selfsame outdoor latitude like.

**(QR-5)**Using algebraic techniques we feel well-informed, discover the**completion latitude****predicted by the quadratic design **and discover the**term when it occurred.** Report the term to the direct locality hour (i.e., __:00 or __:15 or __:30 or __:45). (For request, a term of 18.25 hours is reported as 6:15 pm.) Report the completion latitude to the direct tenth of a measure. **Show performance.**

**(QR-6)**Use the quadratic polynomial contemporaneously delay algebra to**like the term(s) of day when the outdoor latitude is a feature target latitude. **Each collocate portion accomplish performance delay a unanalogous target latitude, assigned by your tutor. Report the term(s) to the direct locality hour. Be confident to use the quadratic design to effect the term likes (not esteems in the postulates board). **Show performance.** Recite your results perspicuously -- the target latitude and the associated term(s).**Show performance.**

** **

**Tasks for Exponential Retreat Design (ER)**

**(ER-1)**Plot the points (*x*,*y*) in the remedy board (Table 2) to get a**scatterplot**. Note that the bear is definitely non-linear. Use an alienate lamina on the tame and upright axes and be confident to write carefully.

**(ER-2)**Find the**exponential character of best fit**and**graph**it on the scatterplot. Recite the**formula**for the exponential character. It should feel the form*y*=*A**e*^{-bx} where software has supposing you delay the numerical esteems for*A*and*b*.

**(ER-3)**Find and recite the esteem of**r**** ^{2}**, the coefficient of gratification. Discuss your discoverings.(

*r*

^{2}is adapted using a unanalogous formula than for rectirectirectistraight retreat. However, sound as in the rectirectirectistraight request, the closer

*r*

^{2}is to 1, the amend the fit.) Is an exponential flexion a amiable flexion to fit to this postulates?

**(ER-4)**Use the exponential character to effect a**coffee latitude****estimate**. Each collocate portion accomplish calculate a latitude like for a unanalogous gone-by term *x* assigned by your tutor. Substitute your*x*esteem into your exponential character to get*y*, the selfsame latitude variety among the coffee latitude and the ground latitude. Since*y*=*T*- 69, we feel coffee latitude*T*=*y*+ 69. Take your*y*like and add 69 measures to get the coffee latitude like. Recite your results perspicuously -- the gone-by term and the selfsame like of the coffee latitude.

**(ER-5)**Use the exponential character contemporaneously delay algebra to**like the gone-by term when the coffee landd at a feature target latitude**. Report the gone-by term to the direct tenth of a microscopic. Each collocate portion accomplish performance delay a unanalogous target coffee latitude *T* assigned by your tutor.

Given your target latitude *T*, then*y*=*T*- 69 is your target latitude *difference* among the coffee and ground latitudes. Use your exponential design *y*=*A**e*^{-bx}. Substitute your target latitude variety for *y* and unfold the equation*y*=*A**e*^{-bx}for gone-by term *x. ***Show algebraic performance**in solving your equation. Recite your results perspicuously -- your target latitude and the liked gone-by term, to the direct tenth of a microscopic.

For request, if the target coffee latitude*T*= 150 measures, then *y* = 150 - 69 = 81 measures is the latitude *difference* among the coffee and the ground, what we are calling*y*. So, for this feature target coffee latitude of 150 measures, the motive is discovering how covet it took for the latitude variety*y*to land at 81 measures; that is, solving the equation 81 =*A**e*^{-bx}for*x*.