Determine wherher the equation y=e^-x could represent exponential growth, decay or neither.

Q: A colony of bacteria is growing exponentially. At time t = 0 minutes it has 300 bacteria in it, and…

A: Let's Solve,

Q: Two quantities increase exponentially with growth constants k = 1.2 and k = 3.4, respectively. Which…

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Q: The half-life of Erbium-171 is 7.5 hours. What is the hourly decay rate? Express the result to four…

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Q: Suppose that fis an exponential function with percentage decay rate of 5% and that f(0) = 9. Find a…

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Q: The half-life of a substance is 1200 years. If the initial amount of the substance is 300 grams,…

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Q: A certain radioactive element decomposses at a rate proportional to the amount present. If 100…

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Q: A population is known to grow exponentially. If it starts at 100 and is 150 after 3 months when will…

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Q: A student is 19 years old and the world has a population of 6.6 billion. Assuming that the…

A: Given Present population (P) = 6.6 Rate (R) = 0.6% Time  (n) = 72-19= 53

Q: A bird species in danger of extinction has a population that is decreasing exponentially A = A0ekt.…

A: Given A=A0ekt Initial population = 1400 when t = 0 after 5 years population is 1000

Q: The size of a threatened population of bottlenosed dolphins is decaying exponentially with a…

A: topic - exponential function

Q: Show that a radioactive substance which exponentially decays to 20% of its initial value after 8…

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Q: After 245 years half of a sample of radioactive element remains. Write the equation for modeling its…

A: First form the differential equation than solve it.

Q: A quantity with an initial value of 980 decays exponentially at a rate of o.3% every decades. What…

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Q: The rate of a continuous money flow starts at ​$600 and increases exponentially at 4% per year for…

A: Given, Initial amount P0 = $600 R = 4% = 0.04 T = 15 years

Q: The number of women graduating from​ 4-yr colleges in a particular country grew…

A: let the exponential function is   P(t) =P0 ert

Q: In 2000, the population of Israel was approximately 6.04 million and by 2050 it is projected to grow…

A: The explicit form of the exponential growth model is defined as At=A0ekt. Where, A(t) denotes the…

Q: Determine how much time is required for an investment to triple in value if interest is earned at…

A: Let P be the principal amount, then the triple amount of P is 3P.

Q: Suppose a new mosquito-borne virus has emerged and has caused 550 cases to- date. The number of…

A: A = A0(e-kt)  Where , k = Rate , t = time

Q: The U.S. Census Bureau keeps a running clock totaling the U.S. population. On September 20, 2012,…

A: Consider t be the time in years after the September 20, 2012 at 8.11 p.m. EST and y(t) be the…

Q: The drug Valium is eliminated from the bloodstream exponentially with a half life of 36 hours.…

A: The formula for Valium level a time t is given by N(t)) = N0 e-λt Given initial dose N0 = 20mg t1/2…

Q: A tumor is injected with 0.9 grams of Iodine-125, which has a decay rate of 1.15% per day. How do…

A: Consider the given information ,tumor is injected with 0.9gm

Q: Create two exponential functions that have a horizontal asymptote at y=3 and go through the point…

A: The solution is given below

Q: Determine how long it will take for an initial investment to double if it earns 7% interest per year…

A: The time take to double the initial investment is approximately 10 years  see the calculation below

Q: The population of Japan is decreasing at a rate of about .26% per year. Construct an exponential…

A: Let, The initial population of Japan at t=0 = Po Rate of decreasing = 0.26%

Q: A radioactive substance used in nuclear weapons decays at the rate of 3.2% per year. Calculate the…

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Q: see attached

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Q: A bird species in danger of extinction has a population that is decreasing exponentially (A =…

A: Given population equation - A = A0ekt                ................(1)A0 = Initial Population =…

Q: The number of women graduating from 4-yr colleges in a particular country grew from 1930, when…

A: Let N(t)=Cekt...........Equation (A)   Given- In year 1930, 48,829 women earned a bachelor's degree…

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

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Q: Explain the difference between an exponential growth model and a logistic growth model.

A: Explain the difference between an exponential growth model and a logistic growth model as follows.

Q: proportional to A, weight W, and height H. A and W measurement values taken from different people…

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Q: A city has 1000 individuals and its population doubles every 60 years. Give an exponential model for…

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Q: A material has an initial of 15 units. Which equation models the amount of the material y, decaying…

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Q: A biologist has 6827 gram sample of a radioactive substance. Find the mass of the sample after four…

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Q: If 26 grams of radioactive waste reduces to 19.35 grams of radioactive waste after 1120 years, then…

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Q: A quantity with an initial value of 510 grows exponentially at a rate such that the quantity doubles…

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Q: When you moved into your dorm room, there were initially 40 termites. After 6 days, there were 125…

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Q: How is Calculus used to derive the exponential growth or decay model?

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Q: Suppose that a population that is growing exponentially increases from 800,000 people in 2010 to…

A: the exponential model is of the form, At=A0ekt where A0 original amount of the entity, t is the…

Q: Suppose a variable is growing continuously at a nominal rate of 10% per year. What is the effective…

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Q: A sample of bacteria taken from a river has an initial concentrationof 2.5million bacteria per…

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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: A quantity with an initial value of 390 decays exponentially at a rate of 8.5% every 9 weeks. What…

A: We give the change of the quantity as a function of time as y(t)=390 e-0.0859t where t is in weeks.

Q: An endangered species of fish has a population that is decreasing exponentially. The population 5…

A: We will use concept of exponential growth.

Q: The rate of auto thefts doubles every 6 months. Determine, to two decimal places, the base b for an…

A: We have to find base b and  tripling time to the nearest tenth of a month.

Q: How do we distinguish between exponential growth and exponential decay functions?

A: For the given problem, we have to distinguish between exponential growth and exponential decay…

Q: Jun has decided to save money roughly P25 per week. Suppose he makes weekly deposits of this money…

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Q: Due to the rising temperatures in a bay ecosystem, the population mass of a certain species of…

A: We have given x(0)=600 tonsx(11)=2,000 tons population increase at…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.