8. There are 50 mg of a certain chemical substance and it is expected that the substance will be half this size in 5 years. Create an exponential model for the amount of the substance remaining in t years. 9. A colony of bees doubles in size every six months. If there are initially 5000 bees, Create a model for the bee population P where t represents the number of months that have passed.

Q: 100mg sample of tritium-3 decayed to 94.5mg after a year. (i) What is the half-life of tritium-3?…

A:

Q: 4. How much should be invested at 12.5% compounded continuously to end up with $1000 at the end of 5…

A:

Q: The half-life of cobalt 60 is 5 years. (a) Obtain an exponential decay model for cobalt 60 in the…

A: (a) It is given that the half life of cobalt 60 is 5 years. The exponential decay model for cobalt…

Q: 12. If the graph of the exponential function f(x) = a", where a > 0 and a + 1, is decreasing, then a…

A: If the graph of the exponential function fx=ax, where a>0 and a≠1, is decreasing, then a must be…

Q: Suppose a sample of a certain substance decayed to 77.4% of its original amount after 300 days.…

A:

Q: 1. Suppose a population of rabbits starts with 30 rabbits. 60 days later, the population is 120…

A:

Q: 3. How long will it take $5000 to triple if it is invested at 7.5% compounded continuously?

A:

Q: 1. The population of a community is known to increase at a rate proportional to the number of people…

A: Topic:- exponential function

Q: 1. A certain species of virus is increasing in number exponentially every hour. The initial virus…

A: To find growth rate of the virus.

Q: 6. Suppose that a fish population t days from now can be modeled by an exponential function P(t) =…

A:

Q: 6. A sample of tritum-3 decayed to 94.5% of its original amount after a year. (a) What is the…

A: A sample of tritum-3 decayed to 94.5% of its original amount after a year. Note:   Multiple…

Q: 1. The population of Kuhala Island doubles every 3 decades. 2. The amount of radioactive isotope of…

A: Whether each given is an exponential function, exponential equation, or exponential inequality or…

Q: Suppose that the half-life of a cesium is 30 years. If there were initially 1000 g of the substance…

A:

Q: 1. Suppose that an equation for investments and savings is described by an exponential function:…

A: Please like my answer

Q: 4 Find a formula for the exponential function passing through the points 3, 27 and (1, 12). y =…

A:

Q: 18. Suppose $7,800 is invested in an account at an annual interest rate of 4.3% compounded…

A:

Q: 1. A radioactive substance has a half-life of 1620 years. a. If its mass is now 4 g (grams), how…

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Q: 2. Suppose that we initially have 500 mg of a radio-active substance as sample. After a year, the…

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Q: 3. A radioactive substance has a half-life of 1620 years. If its mass is now 4 grams, find the time…

A:

Q: 1. A certain radioactive material follows the law of exponential growth. If between noon and 2 pm…

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: Find the exponential growth equation for a population that doubles in size every unit of time and…

A: Given: At time, t=0, No. of individuals=20.

Q: 8) A bacterial culture has an initial population of 10,000. If its population declines to 3000 in 8…

A: Exponential model of population is given by,     P(t) = Po * e^(kt).

Q: The amount of caffeine in the body after consumption follows an exponential decay model. After…

A: 1) The time taken to decay half of the amount of the substance taken initially is called the…

Q: 11) Suppose that $4000 is invested at an interest rate of 5.8% per year, compounded continuously.…

A: We can find the answer for question-11 as below.

Q: 4. The population of a trading area is currently 100 thousand. At time t years from now population…

A:

Q: 1. A certain species of virus is increasing in number exponentially every hour. The initial virus…

A: We will apply exponential growth formula to solve this question

Q: 11 The population of a city is 51,000 and is decreasing at a rate of 1.75% per year. Use an…

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: 2-Suppose that the half-life of a certain radioactive substance is 2 days and there are 50g…

A: After each half life the amount left will be half the initial amount.

Q: practice question 18

A: P0= Initial amount = 2700r= interest rate = 6.8% =0.068t= time = ?P(t)= Final amount = 2700 times 2=…

Q: (3) Suppose we invested $20,000 at an annual rate of 5% where interest is compounded continuously.…

A: The main objective is to frame differential equation and solve them by using initial condition.

Q: 3. If a radioactive substance is quickly decaying at a rate of 13% per hour approximately how much…

A:

Q: 6. Determine the initial amount of radioactive substance if after 22 years, the remaining…

A: To find the initial amount of radioactive substance, decay rate and half-life of the substance.

Q: 1. Strontium-90, 90Sr, has a half-life of 29 years. a) If 42.5 grams remain after 50 years, what is…

A: The formula for the quantity remaining of a substance after t years is: Nt=N012tt12 Here, t12=…

Q: Following the birth of a child, a parent wants to make an initial investment P, that will grow to…

A: Given Initial amountP=P0 Interest rater=6%=0.06 Time t=18 years Future valueA=70,000

Q: 2. Suppose a nuclear accident releases 50 kilograms of the element Cesium 137. If the half life of…

A: Given- Intial amount of Cesium-137 is 50 kg and half life is 30 years. To find- The amount after 30…

Q: 4. A colony of bacteria is growing exponentially. At time t-2 it has l10 bacteria in it, and at time…

A:

Q: 1. The population of a certain barangay is increasing at a rate proportional to its current…

A:

Q: 1. The rate of decay of radium is said to be proportional to the amount of radium present. If the…

A: Since you posted two questions here, i can answer only first one at a time. Please repost other…

Q: Suppose a sample of a certain substance decayed to 79.6% of its original amount after 300 days.…

A:

Q: An endangered species numbered 7,000 at the start of the year 2003 and at the start of 2014 numbered…

A: Given that: An endangered species numbered 7,000 at the start of the year 2003 At the start of 2014…

Q: a) If an investment grows in value at 2.4% per year, how long will it take for its value to double?…

A:

Q: 1. Suppose that the number of bacteria in a certain population increases according to a continuous…

A:

Q: 1. The radioactive isotope hydrogen-3 has a half-life of 12.3 years. a. If a sample of 80 mg of…

A:

Q: 9. A sample of tritium-3 decayed to 94.5% of its original amount after a year (a) What is the…

A: Consider N (t) is the amount of tritium-3 relative to the original amount, then general form is,

Q: Scientists have observed that a small colony of penguins on a remote Antarctic Island obeys the…

A: We know that, P= P0ert where P is the population at time t. P0 is the initial population. r is the…

Q: The annual usage time of the device whose failure time follows the exponential distribution is 1,000…

A:

Q: 1. Initially, there are 150 grams of radioactive element and in 2550 years there will be 60 grams…

A:

Q: me mass of a radioactive substance follows a continuous exponential decay model, with a decay rate…

A: Topic:- function

Q: If a population of is becoming extinct and the population is decaying exponentially. Assume that…

A: From given information

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.