The population of a southern city follows the exponential law. Use this information to answer parts a and b T (a) If N is the population of the city and t is the time in years, express N as a function of t N(t)= No en kt (Type an expression using t as the variable and in terms of e.) (b) If the population doubled in size over 30 months and the current population is 40,000, what will the population be 3 years from now? The population will be approximately people. (Do not round until the final answer. Then round to the nearest whole number as needed.)

The population of a southern city follows the exponential law. Use this information to answer parts a and b T (a) If N is the population of the city and t is the time in years, express N as a function of t N(t)= No en kt (Type an expression using t as the variable and in terms of e.) (b) If the population doubled in size over 30 months and the current population is 40,000, what will the population be 3 years from now? The population will be approximately people. (Do not round until the final answer. Then round to the nearest whole number as needed.)

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

The effect of changing the growth rate variable, r, in an exponential function. If aninitial population Po grows at r% per year, the population in t years is given by thefunction P(b) - Pa(2) *2*. Suppose that a city has 400,000 people currently, and thepopulation is projected to grow at 1% annually for the next 30 years. Find thepopulation in 30 years. The growth rate has to be written as a decimal, notpercentage.)
If f(æ) = Aek is an exponential function with f(-4) = 10 and f(0) = 2, then what are A and k?
(Depreciation). Table 2 gives the market value of a luxury sedan (in dollars) x years after its purchase. (Use 4 decimal places in all answers.) Table 2: Luxury Sedan's Value x Value ($) 1 23,125 2 19,050 3 15,625 4 11,875 5 9,450 6 7,125 A. What exponential equation, V(x) best fits the data, where x is the number of years after purchase and V(x) is value of the vehicle after x years?V(x) = B. What is r2?r2 = C. Use the equation to estimate the purchase price of the vehicle and the value of the vehicle after 10 years. (Round to the nearest cent.)The purchase price of the vehicle after 10 years will be $ .D. Use the equation to estimate how old a luxury sedan valued at $12,000 is. (Round to the nearest year.)The luxury sedan should be about years old.
A lush forest has 100 foxes and 2 rabbits. The fox population doubles every year and the rabbit population triples every year. The foxes agree not to hunt the rabbits until they are outnumbered by the rabbits. -Let t be the number of years that pass, and come up with two exponential expressions that model the fox population and rabbit population respectively. -The rabbits will equal (and then shortly outnumber) the foxes midway through some year. Find the value of t such that the two populations are equal, accurate to four decimal places, and the populations of each animal at that time to the nearest whole number.
The graph (in the attached picture) shows four exponential functions, each with the equation; y = abx If a > 1 and b > 1, then which of four (in the attached picture) could be its graph?
A population numbers 19,000 organisms initially and decreases by 2.1% each year. Suppose P represents population, and t the number of years of growth. An exponential model for the population can be written in the form P= ab where P =
A national census bureau predicts that a certain population will increase from 35.3 million in 2000 to 64.3 million in 2060. Complete parts (a) through (c) below. (a) Find an exponential function of the form f(t) = y₁b¹ for these data, in which t= 0 corresponds to 2000 and f(t) is in millions. f(t) (Use integers or decimals for any numbers in the expression. Round to four decimal places as needed.) (b) What is the projected population in 2030? In 2040? = In 2030, the population is projected to be (Round to one decimal place as needed.) million. million. In 2040, the population is projected to be (Round to one decimal place as needed.) (c) By experimenting with different values of t (or by using a graphing calculator to solve an appropriate equation), estimate the first full year in which the population will exceed 56 million. The first full year in which the population will exceed 56 million is
Find the asymptote of the given exponential function y = 2*-3 + 8 1 2 -3 8
In 2011, the population of Canada was about 34.34 million. For the years 2011 through 2021, the population is projected to grow at a rate of about 1.1% per year. (a) Find a formula for an exponential function that gives the population of Canada. (Let N be the population in millions and t be the number of year since 2011.) N(t) = (b) Express, using functional notation, the population of Canada in 2017. NO Calculate that value. (Round your answer to two decimal places.) million (c) Use the function you found in part (a) to predict when the population of Canada will reach 37.5 million. (Round your answer to two decimal places.) years after 2011