The number of Americans age 65 or older can be modeled as n(x) = −0.00082x3 + 0.059x2 + 0.183x + 34.42 where output is measured in million people and x is the number of years since 2000, projections through 2050. What is the rate of change of the projected number in 2045? Calculate the percentage rate of change in the projected number in 2045.

Q: Pilar owns a parcel of land whose value tyears from now will be V (t) = 8000e" dollars. If the…

A: Given: Pilar owns a parcel of land whose value t years from now will be V(t) = 8000et dollars. The…

Q: The radioactive isotope of lead Pb-209, decays at a rate proportional to the amount present at any…

A: The differential equation for decay is dAdt=kA dAA=k·dt ⇒∫dAA=∫k·dt⇒lnA=kt+c1A=ekt+c1A=ektec1A=Cekt…

Q: The number of insects in a colony is known to multiply at a rate proportional to the number of…

A:

Q: Can the average rate of change of an increasing function ever be negative?

A:

Q: The population of a certain country has grown at a rate proportional to the number of people in the…

A: Given, the population of a certain country has grown at a rate proportionalto the number of people…

Q: Because of job outsourcing, a town predicts that its public school population will decrease at the…

A: Proceed as shown below...

Q: Estimate the average rate of change for the graph above from x=1x=1 to x=4

A:

Q: What is the rate of change for h(x) = 8x - 9 on the interval [1, 4]?

A:

Q: The population of Glenbrook is 375,000 and is increasing at the rate of 2.25% per year. Predict when…

A: Given:The population of Glenbrook is 375,000 and is increasing at the rate of 2.25% per year.…

Q: The median selling price of an existing home in the United States increasing continuously over the…

A:

Q: What is a related-rate equation?

A:

Q: A machine costing P45,000 is estimated to have a salvage value of 14,350 when retired at the end of…

A:

Q: Initially 87 grams of radioactive substance was present. After 3 hours the mass had decreased by 6%.…

A: From the rule of decay that is, the rate of decay is proportional to the amount of the substance…

Q: You have a large metal box filled with honey, where the width is 14 cm, the length is half its size,…

A: For the metal box, it is given that width is b=14 cm, Length is half of width, l=7 cm,  Volume is…

Q: Find the equation of the graph and estimate the instantaneous rate of change at x = 1

A: From graph we can conclude that the equation of this graph be a parabola i.e., a quadratic equation.…

Q: Suppose that the boy’s weight was increasing at the rate of 7 kilograms per year and his height was…

A: We know that, BMI=Bodyweight in kilogramHeight in meters2⇒B=wh2

Q: Estimate the average rate of change from x = 1 to x = 4. %3D

A: average rate of change of f(x) on a,b=f(b)-f(a)b-aHere a=1 ,  b=4From graph f(1) = 5 ,  f(4) = 4

Q: In the year 1985, a house was valued at $108,000. By the year 2005, the value had appreciated to…

A:

Q: Suppose the amount of oil pumped from one ofthe canyon wells in Whittier, California, decreases at…

A: We know that general exponential function is  y=y0e-kt California, decreases at the continuous rate…

Q: The city of San Estaban had a population of 45,000 in 2015 (t=0) and was growing continuously at an…

A: Initial population =45000 Growth Rate=3%=0.03 At 2016, t=2016-2015=1 So the population in 2016 is:

Q: Consider the constant rate of depreciation value of a certain car. You bought a car amounting to 1.5…

A: Solution

Q: 8. Create the equation of any function where the instantaneous rate of change when x = 1 does not…

A: Create the equation of any function where the instantaneous rate of change when x = 1 does not…

Q: Find the average rate of increase in population which in the first decade has increased by 20%, in…

A:

Q: In the year 1985, a house was valued at $108,000. By the year 2005, the value had appreciated to…

A:

Q: 14. Find the rate of change of y= (2x' +6x +4) at x =-1.

A:

Q: An amplifire is having a gain of 500 without feedback.If negative feedback is applied.the gain is…

A: Given:    Av   =  500    Avf   = 100

Q: Initially 50 grams of radioactive substance was present. After 10 hours the mass had decreased by…

A: The rate of change of amount A with respect to time t can be denoted by dAdt. If x is directly…

Q: Estimate the average rate of change from x = 4 to x = 7.

A: The average rate of change from one point to another point from a graph obtains from the ratio of…

Q: The rate of decomposition of radioactive radium is proportional to the amount present at any time.…

A: The rate of decomposition is proportional to y, we know that y=Cekt, where t is the time in years.…

Q: The population of Jefferson City is 95,000. Assuming a growth rate of 2.5% pee year, what will the…

A: Given that population of Jefferson city is P=95,000.  growth rate is R=2.5% per year we have to find…

Q: The number of U.S. citizens aged 65 years and older from 1900 through 2050 is estimated to be…

A:

Q: the instantaneous weight growth rate at week 16 greater or smaller or the same than the average rate…

A: Given query is to provide information regarding instantaneous rate of change and average rate of…

Q: The population of Glenbrook is 375,000and is increasing at the rate of 2.25% per year. Predict when…

A: To find: When the population is 1 million. Given: Initial population is 375000 and rate of…

Q: The population of Tagum City is increasing at the rate proportional to its current population. In…

A:

Q: A particle is moving along the graph of the equation y = x* + 2x -5x - 85. If the abscissa is…

A:

Q: Suppose an unknown radioactive substance produces 800 counts per minute on a Geiger counter at a…

A:

Q: A house was valued at $190,000 in the year 1988. The value appreciated to $250,000 by the year 2003.…

A: House Price was 1,90,000 in year 1988. P=$1,19,000 The value appreciated to $250,000 by the year…

Q: Suppose the amount of oil pumped from one of the canyon wells in Whittier, California, decreases at…

A: To determine the time (in years), the output of well fall to 1/5 of its present value.

Q: A biology experiment begins with 5 cells. In four days, the experiment grows to 164 cells. Assuming…

A:

Q: How are the rate constant and the doubling time related?

A: Explanation: The exponential growth function is y(t)=y0ekt where k  is the positive constant rate…

Q: Assume the rate at which the zombies spread is jointly proportional to the number of encounters…

A: Please check next steps for the solution.!

Q: How may I get the average rate of change for this problem?

A: The average rate of change of the function fx between the two points x=a and x=b is given by the…

Q: If a new car is valued at $20,600 and 8 years later it is valued at $3000​, then what is the average…

A: Given that the value of a new car is $20,600 and 8 years later it is valued $3,000.The initial value…

Q: Suppose that the amount of water pumped from a water well decreases at a continuous rate of 10% per…

A:

Q: Estimate the average rate of change from  x = 2  to  x = 5.

A: We are given a graph of a function and we are asked to find average rate of change from x=2 to x=5.…

Q: If f(x) = 12x2 − x3, what is the rate of change of f '(x) at  (−1, 13)?

A:

Q: The price of a computer component is decreasing at a rate of 13​% per year. State whether this…

A: The price of a computer component is decreasing at 13% per year. Now, let the initial price of the…

Q: Initially 87 grams of radioactive substance was present. After 3 hours the mass had decreased by 6%.…

A: We know that the differential equation of the decaydAdt=kAwhere A = amount and k = proportionality…

Q: Consider the constant rate of depreciation value of a certain car. You bought a car amounting to 1.5…

A:

Q: a 2012 article in the Los Angeles times reported that the number of weekly visits to Pinterests web…

A: The number of visitors in the year 2011 = 1.27 million Percentage increase = 2183% every year So the…

Exponential Growth Model

The relation that represents an exponential function is: