How do I solve this 1. Find derivativey = (8x²-3x²) ³2. Find derivative of given function defined as fillowsy=e- 2xgiven function defined as follows. 7-29-223. write given exponential function in Jogarithmic form52 254 write given logarithmic equation in exponential form81log 35. Evaluate given logarithm without using a calculatorвода816. Find the derivative ofY= LN (-4x)givenfunction defined as follows

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Answered: 1. Find derivative of given function…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.7: Applications

Problem 14EQ

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Suppose that $12,000 is invested in a saving account paying 5.6% interest per year. (a)Write the formula for the amount in the account after t years if interest is compounded monthly. (b)Find the amount in the after 3 years if interest is compounded daily. (c)How long will it take for the amount in the account to grow to $20,000 if interest iscompounded continuously?
Suppose that a particular pond can sustain up to 30,000 tilapia and that the undisturbed population of tilapia in this environment can be modeled according to the logistic model as dP/dt = 4(1 - P/30,000)P. Suppose that the farmer wishes to sell 15,000 fish per year. In this case, the harvest model will be constant. a. Following the constant harvest model, write an equation, involving a derivative, that governs the population of tilapia. b. What happens to the population if P = 5000? c. What happens to the population if P = 20,000? d. Find the two equilibria for this model.
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? deer
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.
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a certain strain of bacteria is placed in a petri dish as a part of an experiment. The number of bacteria present in the petri dish, b(t), grows exponentially as a function of t, where t is measured in minutes since the start of the experiment. However, the lab assistant carelessly forgot to measure the number of bacteria at the start of the experiment. If there are 600 bacteria present after 1 minute and 900 bacteria present after 3 minutes, model the number of bacteria b(t) as an exponential function of t
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2log x-1=log(x-1)

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1. Find derivative of given function defined as follows. 7-29-22 y = (8x²-3x³) ³