A colony of bacteria that grows according to the law of uninhibited growth is modeled by the function N(t)=100e0.045t where N is measured in grams and t is measured in days. (a) Determine the initial amount of bacteria. (b) What is the growth rate of the bacteria? (c) What is the population after 5 days? (d) How long will it take for the population to reach 140 grams? (e) What is the doubling time for the population?

Q: Suppose the population of fish in a lake is modeled by the function P = 442e0.034t, where t is…

A: topic - exponential function

Q: If a cup of coffee has temperature 100°C in a room where the ambient air temperature is 20°C, then,…

A: Solve for average temperature after 40 min.

Q: A colony of bacteria is growing exponentially with growth constant k = 0.25. (a) Determine the rate…

A: Given bacteria population rate and bacteria population functions are

Q: A population of bacteria grows according to the law of uninhibited growth, A(t) = A0ekt. Initially,…

A: The population of bacteria is given by: A(t)=A0ekt where: A0: Initial population of bacteriak:…

Q: A population shows growth that is proportional to the number of inhabitants existing at a given…

A: a)Since the population growth is proportional to the number of inhabitants existing at a given time,…

Q: An unknown radioactive element decays into non-radioactive substances. In 220 days the radioactivity…

A:

Q: A radioactive substance decays at a continuous rate of 14% per year, and 50 mg of the substance is…

A: Solution:a Given that a radioactive substance decays at a continuous rate      of 14% per year and…

Q: Suppose a population grows according to the model P(t) = Po(1.092) where t is measured in years. (a)…

A:

Q: S%3200000 e° find the growth rate of S.

A: Given query is to find the growth rate.

Q: An unknown radioactive element decays into non-radioactive substances. In 100 days the radioactivity…

A: Formula for the radioactive decay is  N=N0e-λt where  N0 is the initial amount N is amount after…

Q: The motion of an particle follows an exponential function s(t)=et. (a) Determine the velocity of the…

A: If the distance function is differentiated with respect to the time, then the velocity function is…

Q: A study of the annual population of butterflies in a county park shows the population, B(t), can be…

A:

Q: An initial population of 250 bacteria in a laboratory experiment increases at an hourly percent…

A: An initial population of 250 bacteria in a laboratory experiment increases at an hourly percent…

Q: ioactive plutonium has a half life of 24,100 years. The mass of plutonium in a sample (in g) present…

A:

Q: Express the exponential function as a power of e. Find the domain and range (а) у -3' -1 (b) у -4'-1

A: We know that, ax=exlna         ⋯⋯1 (a) We have, y=3t-1 By using equation (1) and on solving further,…

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.