Question 24 The population of Sebastian can be modeled by the function \[ P=25677 e^{0.02127 t} \] where \( t \) is the number of years since 2020. Use the above function to answer the following questions. What was the population of Sebastian in 2020? \( \square \) In what year is the population of Sebastian projected to reach 42,110 ? Round the solution to the nearest whole number. \( \square \) Submit and End
Added by Donald C.
Close
Step 1
- Since \( t = 0 \) in the year 2020, substitute \( t = 0 \) into the function: \[ P = 25677 e^{0.02127 \times 0} = 25677 e^0 = 25677 \times 1 = 25677 \] - The population of Sebastian in 2020 was 25,677. Show more…
Show all steps
Your feedback will help us improve your experience
Danielle Fairburn and 62 other Algebra 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
According to the 2010 U.S. census, the population of Sebastian was 21,869. The 2020 U.S. census found that the population of Sebastian had grown to 25,544. Use the exponential growth model Y = Y0 * e^(kt) where t is the number of years after 2010, to write the exponential growth function for the city. Round the growth constant (k) to four significant figures. The exponential growth function that models the population of Sebastian is Use the population growth model to predict the population of Sebastian in the year 2040. Round the solution to the nearest whole number. The model predicts that the population of Sebastian in 2040 will be Determine the year when the model predicts the population of Sebastian will be 43,268. Round the solution to the nearest whole number. According to the model, the population of Sebastian will be 43,268 in the year
James K.
The populations P (in thousands) of a particular county from 1971 through 2014 can be modeled by P = 71.5e0.0319t where t represents the year, with t = 1 corresponding to 1971. (a) Use the model to complete the table. (Round your answers to the nearest whole number.) Year Population 1980 1990 2000 2010 (b) According to the model, when will the population of the county reach 360,000? (c) Do you think the model is valid for long-term predictions of the population? Explain. Yes, the population will continue to grow at this quick rate.Yes, the population will not continue to grow at this quick rate. No, the population will not continue to grow at this quick rate.No, the population will continue to grow at this quick rate.Yes, the population doesn't grow or shrink.
William S.
The population P (in thousands) of Orlando, Florida, from 1980 through 2013 can be modeled by P = 130e^0.0204t, where t = 0 corresponds to 1980. (Round your answers to the nearest whole number.) (a) What was the population of Orlando in 2013? people (b) In what year will the population of Orlando reach 370,000?
Recommended Textbooks
Elementary and Intermediate Algebra
Algebra and Trigonometry
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD