On a typical day in May, the air temperature in Cincinnati can be modeled as f(t)=−.8t2+10t+49F∘, where t is the number of hours in since 7 a.m.
Added by Alexander M.
Step 1
8t^2 + 10t + 49 \), where \( t \) is the number of hours since 7 a.m., we can follow these steps: Show more…
Show all steps
Close
Your feedback will help us improve your experience
Madhur L and 86 other Calculus 1 / AB educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
On a typical day in May, the air temperature in Cincinnati can be modeled as f(t) = -.8t^2 + 10t + 49°F, where t is the number of hours since 7 a.m. In this problem, you will select from the dropdown menu below the correct units for each item below. In the next problem, you will compute the numerical values. 1) What are the units of the change from 11:00 am to 4:00 pm? 2) What are the units of the percent change from 11:00 am to 4:00 pm? 3) What are the units of the average rate of change from 11:00 am to 4:00 pm?
Madhur L.
The average monthly high temperature in degrees Fahrenheit in Cincinnati for the first 10 months of the year can be modeled very accurately by the equation $y=-0.21 x^{3}+$ $2.24 x^{2}+2.33 x+33.67,$ where $x$ is the month, with $x=1 \mathrm{cor}$ responding to January. A wedding planner in Cincinnati is asked to set a date in a month where the high temperature is most likely to be close to 75 degrees. What month would be the best choice?
Functions, Graphs, and Models
Using Graphing Calculators
Midwest Temperature The figure shows the temperature values (in ${ }^{\circ} \mathrm{F}$ ) on a typical May day in a certain Midwestern city.The equation of the graph is $$ t(x)=-0.8 x^{2}+11.6 x+38.2^{\circ} \mathrm{F} $$ where $x$ is the number of hours since 6 A.M. a. Write the formula for $t^{\prime}$. b. How quickly is the temperature changing at $10 \mathrm{~A} . \mathrm{M} . ?$ c. What is the instantaneous rate of change of the temperature at $4 \mathrm{PM} . ?$ d. Draw and label tangent lines depicting the results from parts $b$ and $c$
Determining Change: Derivatives
Simple Rate-of-Change Formulas
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD