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given that
h(x) = log_3(2x+5)
which the following is the dervivative h'(x)?
a.1/(2x+5)ln3
b.2/3ln(2x+5)
c.2/(2x+5)ln
d2/2x+5
e.2ln3/2x+5
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- Suppose an investment account is opened with aninitial deposit of 10,500 earning 6.25 interest,compounded continuously. How much will theaccount be warm after 25 years?Recent data suggests that, as of 2013, the rate of growth predicted by Moore’s Law no longer holds. Growth has slowed to a doubling time of approximately three years. Find the new function that takes that longer doubling time into account.An individual improperly disposes of 8 parakeets in a nearby woodland, where they begin to reproduce at an initial rate of 3 parakeets per month. Write a differential equation for the population P assuming logistic growth, where the woodland can support at most 500 parakeets. (Do not round any coefficients.) dP/dt =
- Suppose that a population grows according to a logistic model with carrying capacity 6500 and k = 0.0015 per year. If the initial population is 1000, write a formula for the population after t years.$2000 is invested at a rate of 8% coumpounded continuously. What is the amount at the end of 12 years?When a breeding group of animals is introduced into a restricted area such as a wildlife reserve, the population can be expected to grow rapidly at first but to level out when the population grows to near the maximum that the environment can support. Such growth is known as logistic population growth, and ecologists sometimes use a formula to describe it. The number N of deer present at time t (measured in years since the herd was introduced) on a certain wildlife reserve has been determined by ecologists to be given by the function below. (Round your answers down to the nearest whole number.) N = 12.35 0.01 + 0.54t (a) How many deer were initially on the reserve? deer(b) Calculate N(12).N(12) = deer (c) Express the number of deer present after 17 years using functional notation. N Calculate the number of deer present after 17 years. deer(d) How much increase in the deer population do you expect from the 12th to the 17th year? deer
- When a breeding group of animals is introduced into a restricted area such as a wildlife reserve, the population can be expected to grow rapidly at first but to level out when the population grows to near the maximum that the environment can support. Such growth is known as logistic population growth, and ecologists sometimes use a formula to describe it. The number N of deer present at time t (measured in years since the herd was introduced) on a certain wildlife reserve has been determined by ecologists to be given by the function below. (Round your answers down to the nearest whole number.) N = 12.33 0.01 + 0.54t (a) How many deer were initially on the reserve? deer(b) Calculate N(12).N(12) = deer(c) Express the number of deer present after 17 years using functional notation. N Calculate the number of deer present after 17 years. deer(d) How much increase in the deer population do you expect from the 12th to the 17th year? deerThe total number of reported cases of an illness in a large city days after the start of an outbreak is modeled by the function y = F(t) that is a solution to the logistic differential equation dy/dt= (1/5600)y(1400-y). If there are 5 reported cases of the illness initially, what is the limiting value for the total number of reported cases of the illness as t increases?During the start of the COVID 19 pandemic it is assumed that the rate of spread of the corona virus is 18 % daily following a simple logistic growth model by Verhulst. Ten persons are assumed to have acquired the virus in province X. Assuming province X with a population of 2 million does not follow any necessary protocol to prevent the spread of the virus, approximately how many are expected to have acquired the virus after 30 days?
- Express the following in terms of x without logs or natural logs 1) log100x 2) 1000logx 3) log0.001x 4) ln e2x 5) eln (3x+2) 6) ln (1/e5x) 7) ln √ex4. The population of Lalaland is 600,000 currently and is expected to grow (continuously) at 3.5% per year. Determine what the population will be in 4 decades (i.e. 40 years)?Interest is compounded continuously at 5%. How long until a $5000 investment grows to $12000?
