Concept explainers
(Refer to Exercise 46). Suppose someone initially weighing
a. Write the weight function for this individual.
b. Graph the weight function on the window
c. How long will it take a dieter to reach a weight just
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Calculus For The Life Sciences
- The half-life of plutonium-244 is 80,000,000 years. Find function gives the amount of carbon-14 remaining as a function of time, measured in years.arrow_forwardTable 6 shows the population, in thousands, of harbor seals in the Wadden Sea over the years 1997 to 2012. a. Let x represent time in years starting with x=0 for the year 1997. Let y represent the number of seals in thousands. Use logistic regression to fit a model to these data. b. Use the model to predict the seal population for the year 2020. c. To the nearest whole number, what is the limiting value of this model?arrow_forwardGlobal temperature increases are benchmarked to the average temperature between 1951 and 1980. In 2010, the global average temperature was 0.72°C above the benchmark. In 2020, it was 1.02°C above.1 1climate.nasa.gov, accessed March 23, 2021. (a) Assuming the difference between the global average temperature and the benchmark is a linear function of time, find a formula for this function. The increase in average global temperature, G, above the benchmark average in the year t is given by G = i i )t eTextbook and Media (b) Use this formula to predict the difference in 2027. °C The formula predicts that in the year 2027, the average global temperature will have increased by over the benchmark.arrow_forward
- 8. The percent p a stock price has fluctuated in one year can be modeled by p(x) = 0.0005x+ - 0.0193x³ + 0.243x² - 1.014x + 1.04, where x is the number of months since January. a. Use a graphing calculator to graph the function. b. State the relevant domain and estimate the range c. Use the graph to approximate the y-intercept. Then find the y- intercept algebraically. What does the y-intercept represent? d. Find and interpret any zeros of the function.arrow_forwardI need help with the first fourarrow_forwardPopulation of Barangay X Year 2010 2011 2012 2013 2014 2015 Population 20,531 21,935 23,436 25,034 26,751 28,581 Instructions: 1. Find the rate of increase of population in Barangay X from 2010 to 2015. (round off answer up to two decimal places) 2. Determine the Function that models the population change of Barangay X from 2010 to 2015. 3. Sketch the graph of the function and plot also the points corresponding to the actual population. 4. Estimate the expected population of Barangay X by the end of 2020. 5. Determine approximately the year when the population of Barangay X reaches 60,000.arrow_forward
- 1956, M. King Hubbert proposed a model to analyze crude oil production. His model, with updated data, gives world crude oil pro 254.43e-0.0421 (1 + 2.12e-0.0422 lere P is measured in billions of barrels per year, and t is time, in years, since 2000. (a) Make a graph of world crude oil production for 2000 through 2040. P P P= 35 30 25 20 15 10 5 P 35 30 25 20 15 10 5 10 10 20 20 30 30 40 t 40 35 30 25 20 15 10 O 5 to 35 30 25 20 15 10 202 P 5 10 10 20 20 30 30 40 40 t t (b) In what year does this model predict a peak in world crude oil production? (Round your answer to the nearest whole number.) 2000 X (c) What is the maximum crude oil production predicted by this model? (Round your answer to the nearest whole number.) billion barrels per yeararrow_forward2. Let the function Prepresent the population in billions of a country P (t) and represented by the model P (t) = 1.39 (1.006) . Select all of the statements that are true. a. The starting population in 2013 was 1.39 billion. b. In 2031 the population will be approximately 1.55 billion. c. The annual growth rate is 6%. d. Another way to represent the model is P (t) = 1.39 · e0.006t 3. A population of cicadas is modeled by a function defined by f(w) = 250 • e(0.5w) where w is the number of weeks since the population was first measured. a. Rewrite the equation 500 = 250 · e0.5w to isolate w. b. What does w mean in this context? c. How many weeks does it take for the cicada population to double? Show your reasoning.arrow_forwardA graphing calculator is recommended. Straight-line depreciation is a method for estimating the value of an asset (such as a piece of machinery) as it loses value ("depreciates") through use. Given the original price of an asset, its useful lifetime, and its scrap value (its value at the end of its useful lifetime), the value of the asset after t years is given by the formula for 0 ≤ t ≤ (Useful lifetime). (a) A farmer buys a harvester for $40,000 and estimates its useful life to be 20 years, after which its scrap value will be $4000. Use the formula above to find a formula for the value V of the harvester after t years, for 0 ≤ t ≤ 20. (Do not use commas in your answer.) V = Value = Price - (b) Use your formula to find the value of the harvester after 5 years. V(5) = No Solution (c) Graph the function found in part (a) on a graphing calculator on the window [0, 20] by [0, 40,000]. (Hint: Use x instead of t.) Help 40000 30000 Price (Scrap value) (Useful Lifetime) 20000 10000 10 Fill…arrow_forward
- what do i put in the graphing utilityarrow_forwardpage. 1. A bacteria colony initially has 4000 cells and triples every week. A function that can be used to model the population, p, of the colony after t days is a. p(t) = 4000(3)' с. %3D p(t) = 4000(3) 7 b. P(t) = 4000(2) d. p(t) = 4000(2) 7 %3D An investment of $100 is placed into an account that earns interest ompounded onnuolly € 50/ 6C.arrow_forward
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