Some biologists model the number of species S in a fixed area A (such as an island) by the species-area relationship log(S) = log(c) + k log(A) where c and k are positive constants that depend on the type of species and habitat. (a) Solve the equation for S. (b) Using part (a), if k = 3 and the area is tripled, then by what magnitude is the number of species %3D increased?

Q: The population of a culture of bacteria is modeled by the logistic equation P(t)=…

A: (a) To find the number of days it will take for the culture to reach 75% of its carrying capacity:…

Q: Suppose an Egyptian mummy is discovered in which the amount of carbon-14 present is only about…

A: Decay of amount of carbon 14 is given by y(t) = yo e-0.0001216 t where yo is the amount of carbon 14…

Q: Find the exponential function f(x)=ax whose graph goes through the point (2,4). a =

A:

Q: Find the value of x satisfying log,, (2×+x– 41)=x (1 – log1,5).

A: It is given that, log10(2x+x-41)=x(1-log105)   Here logarithmic properties are going to be useful to…

Q: The number N(t) of people in a community who are exposed to a particular advertisement is governed…

A:

Q: Find a formula for an exponential function y=f(x)  whose graph contains the points (-10,36) and…

A: The general form of the exponential function is:

Q: Find an exponential function of the form f(x) = bax + c for the graph.

A: Given function-  f(x)= bax+c ----(A)  The curve (A)  is passing through ( -1,9) So putting x=-1 and…

Q: Find a formula for the exponential function passing through the points (-2, 2/25) and (3, 250).…

A:

Q: Find a formula for the exponential function passing through the points 3, 27 and (2,18) f(x) =

A: Given:

Q: Solve for x in log,(x+1) + log4(x – 1) = log4 15 . A. x= 5 В. х3 4 C. x= 14 D. x= 3 or x = 1

A:

Q: Find a formula for the exponential function passing through the points (-1,-) and (1,8) y% =

A:

Q: Find the formula for the exponential function passing through the points (0,1.5) and (1,5).

A:

Q: Find a formula for the exponential function passing through the points ( – 3, 160) and (2, 5) f(x) =

A: We are given two points which are (-3, 160) and (2,5). We have to find a formula for the exponential…

Q: 5. Solve for x without using a calculator: log. (x) + log,(x – 16) = 2

A: The answer is found in step-2

Q: 1) Solve for x and y in the following simultaneous equations *a) log, x = 2; 5y= x +12 log, y *b)…

A: We have to solve for x and y in the following simultaneous equations.

Q: The population of an island grows at a rate proportional to its population. If the growth rate is 5%…

A:

Q: Find a formula for the exponential function passing through the points (– 3, 96) and (2, 3) f(x) =

A: Points (-3,96) and (2,3)The general form of an exponential function isgiven by y=abx ---(1)Now the…

Q: Find a formula for the exponential function passing through the points (-2,-) and (1,10) y =

A: On solving this we will asume firstly general exponential function so  we will get

Q: As the base a of an exponential function f(x) = a* , where a>1, increases, what happens to the…

A: As the base a of an exponential function f(x) = ax where a >1, increases To find what happens to…

Q: Find a formula for the exponential function passing through the points (-3, 2 / 27) and (1, 6). y =

A:

Q: A function defined by y = ab can be written in terms of an exponential function base e as

A: The function is y=abx

Q: Find a formula in the form of f(x)=a(b)^x for the exponential function that passes through the two…

A: Consider the exponential formula Given that f(x) passes through the (0,2) and (3,432).

Q: The initial size of a bacteria culture that grows exponentially was 10,000. After 1 day, there are…

A:

Q: In 2003, 182 deer were introduced into a wildlife refuge area from which the population had…

A:

Q: Find a formula for the exponential function passing through the points (- 2, 250) and (1, 2) f(x) =…

A: We have to find a formula for the exponential function passing through the points (-2, 250) and (1,…

Q: Find a formula for the exponential function passing through the points (– 2, 40) and (1, 5) f(z) =

A: Consider the exponential function y=abx. Substitute -2,40  and  1,5 in the above function and obtain…

Q: In particular, the law says that the time, T, it takes to make a choice can be modeled by the…

A: Given T = b.log2(n+1)where n = number of options from which to choose,b = constant number T = time

Q: Solve 2log (√√x) -log(6x - 1) = 0. 1 A X=- 6 B 1 X=- 5 Ⓒx=5 D x=6

A:

Q: Find the exponential function f(x)=a^x that passes through the point (3,343) and has a y-intercept…

A: We have to find the exponential function f(x)=a^x that passes through the point (3,343) and has a…

Q: Find the equation of an exponential function of the form f(x) = a · bº that passes through the…

A:

Q: 2) During the exponential phase, E. coli bacteria in a culture increase in number at a rate…

A:

Q: A population of bacteria, B, can be modeled using the exponential function B (x) = 3 (2)" , where a…

A:

Q: Find the formula for an exponential function that passes through the two points given. (x, y) = (0,…

A:

Q: A population of 15,000 small deer in aspecific region has grown exponentially to 17,000 in 4 years.…

A: We know that exponential equation to express the population growth is, y=y0ekt Where y0 is initial…

Q: A population is now 3000 and is growing exponentiallywith a growth constant of .02, what will be the…

A:

Q: The population, P, of raccoons in a region is modelled by the exponential relation P = Po(2)*/20 ,…

A: Given: The population of the raccoons in a region is modelled by the relation P=P∘(2)t20 Where t is…

Q: The percentage of adult height attained by a boy who is x years old can be modeled by f(x) = 29 +…

A: To find approximate what percentage of his adult height has a boy attained at 10.

Q: Find a formula for the exponential function passing through the points (-2,2/9) and (1,6)

A: Find a formula for the exponential function passing through the points -2,29 and 1,6. Let y=abx be…

Q: a. 4x + 3 = 210 b. 7x - 1 = 3 c. log(8x -15) - log3 = log(2x + 1)   If Karen makes an initial…

A:

Q: If a population grows exponentially at a rate r, the time it will take for the population to double…

A: We can derive the formula for the time it will take for the population to double using the basic…

Q: The solution to the equation log(x) + log(x + 4) = 0 is X = 0 X = 0.2361 %3D X = 4.2355 X = -0.2361

A:

Q: In 2000, the population of Africa was 807 million and by 2011 it had grown to 1052 million. Solve,…

A: Given: In 2000, the population of Africa was 807 million and by 2011 it had grown to 1052 million

Q: Find a formula for the exponential function passing through the points (– 2, 250) and (1, 2) | f(x)…

A:

Q: i. Solve for x: a) 32x-5 = 27 b) log x = log 3 + 2 log 4 ii. If RM 400 is invested for 2…

A: here solve for x a) 32x-5 = 27      32x-5 = 33     here 27 = 33    so now     2x - 5 = 3…

Q: Find a formula for the exponential function passing through the points (-1,3232) and (1,6)   Y= ?

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.