A biologist is modeling an infestation of fire ants. He determines that the area affected by the ants is given by A(n)=k*(1.5)n+c hectares, where n is the number of weeks after the initial observation and k and c are constants. The model is graphed alongside with point (3, 580). a. Using technology, what is the value of k and c? b. Estimate the time taken for the infested area to reach 1000 hectares.

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A: Given:

Q: C = kmaxt² 5 + 2t² + 3.5t

A:

Q: 8. A cheerleader jumping off another cheerleader can be modeled using the equation ht)--2.5 - 10,…

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: use graphs to find approximate solutions.

A: use graphs to find approximate solutions. 2x=5

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Q: A manager has determined that the revenue R(x) (in millions of dollars) made on the sale of…

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A: Question- A farmer finds that if she plants 75 trees per acre, each tree will yield 45 bushels of…

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A:

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A:

Q: Complete the table below to solve the equation 2.5x − 10.5 = 64(0.5x). x f(x) = 2.5x − 10.5 g(x) =…

A: We are authorized to solve only 1 question.

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A: Given ht=−4.9t2+24.5t+1 We have to find the maximum height of the ball and the time of the ball…

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Q: The demand for monorail service in a city in 2005 can be approximated by  q = −4,500p + 43,500…

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A:

Q: A company's profit when it sells x thousand items is predicted to be P(x) = – 2x2 + 880x – 15000. a)…

A: function P(x)=-2x2+880x-15000 is given, Where in begining No items will be Sold.

Q: 3) If a projectile is launched into the air at 29.4 feet per second from a height of 60 feet, its…

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Q: 27)Use the graph to solve: a)/(x) = 0 b) (x)20 4+y=f(x) 彬

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A: Answer

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Q: Farmer Lindsey estimates that after t days, her crop will be increasing at a rate of r(t)  =  15t8 +…

A: Solution ) r (t) = 15t8 + e-0.76t when t = 0 r(0) = 15×(0)8 + e--0.76×0 r(0) = 0 + e0 r(0) = 0 + 1…

Q: at the one-dimensional and n are constants.

A:

Q: A traffic report generated by the city council has determined that traffic increases or decreases…

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Q: A farmer finds that if she plants 65 trees per acre, each tree will yield 45 bushels of fruit. She…

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Q: Based on the difference in y-values, identify the graph as linear, quadratic, exponential, or…

A: Given data,

Q: Between 2005 and 2009, the percentage of people who own a home has changed drastically from state to…

A: Given: Between 2005 and 2009, the percentage of people who own a home has changed drastically from…

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A: Given, f(x)=0.003x2-0.2x+6.48 Where x is the number of years since 1958.

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A:

Q: maximum height of the ball and when does it hit the ground

A:

Q: The number of newspaper copies produced from 1995 to 2002 is given by C = 50t2 - 200t + 10,000,…

A: Here we want to find minimum number of copies of newspaper produced. Here we use application of…

Q: (In billions of dollars per year) can be modeled D'(t) = 841.51 + 815.24t- 189.51?+19.16t where t is…

A: Given

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A: Given: A population of bacteria is growing according to the equation P(t)=1400e0.09t. The value of…

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A:

Q: A shoe company is planning a new brand of walking shoe for the market. Research shows that x, the…

A: A function f(x) is said to be differentiable at x=a where a∈m, n,if: limh→0fa+h-fah A function f is…

Q: A stone is thrown upward and it's height in meters of time t seconds is given by h(t)=-4.9t+25t+2.3…

A:

Q: A computer virus is spreading according to the equation A = 0.5(20'), where t is the time in hours.…

A: Consider the given: The number  A of computer viruses spreading according  to the equation…

Q: The number of photo copies distributed is given by C = 50t² - 200t + 10000, where t is in years.…

A: Here, C=50t2-200t+10,000

Q: A population of bacteria is growing according to the equation P(t)=550e^0.09t Use a graphing…

A: We graph y=550e0.09x and y=894 using a calculator in the same window.

Q: A farmer finds that if she plants 45 trees per acre, each tree will yield 75 bushels of fruit. She…

A:

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.