The populations of termites and spiders in a certain house are growing exponentially. The house contains 110 termites the day you move in. After four days, the house contains 195 termites. Three days after moving in, there are two times as many termites as spiders. Eight days after moving in, there were four times as many termites as spiders.

How long (in days) does it take the population of spiders to triple? (Round your answer to one decimal place.)

Define

Instructions:

After reading Chapter 4 of the textbook, define the following terms:

-System of linear equations

-Solution to a system of equations

-Consistent system of equations

-Inconsistent system of equations

Write a good paragraph with at least 5 sentences using a minimum of 75 words.

Calculate an approximate value of the area of the place inside the curve. (So if you sketch it up (by using WolframAlpha or something else) then you will see that what is sought after is the calculated value of the area that is inside the curve

1 = (40+43)x^2y^2 + y^4 + (1+1)x^4

American General offers a 8 -year annuity with a guaranteed rate of 6.73% compounded annually. How much should you pay for one of these annuities if you want to receive payments of $600 annually over the 8 year period?

5 + (3 * 4)^2 - 2 = 147

            (5 + 3) * 4^2 - 2 = 126

            (5 + 3 )* (4^2 – 2) = 112

            5 + (3 * 4^2) - 2 = 51

1. Which is the correct answer to using the "order of precedence" and why?

the table gives a total U.S expenditure for health services and supplies selected years from 2000 and projected to 2018.

year $(billion)

2000 1264

2002 1498

2004 1733

2006 1976

2008 2227

2010 2458

2012 2746

2014 3107

2016 3556

2018 4086

a. find an exponential function model to these data, with x equal to the number of years after 2000. b) use the model to estimate the U.S expenditure for health services and supplies in 2020.

2.The percent of boys age x or younger who have been seually active are given below.

Age cumulative percent seuual active girls cumulative percent sexual active boys

15 5.4 16.6

16 12.6 28.7

17 27.1 47.9

18 44.0 64.0

19 62.9 77.6

20 73.6 83.0

a). Creat a logarithmic function that model the data using an input equal to the age of the boys.

b) use the model to estimate the percent of boys age 17 or younger who have been seually active

c. compare the percent that are sexually active for the two genders, what do you conclude.

3). if $12000 is invested in an account that pays 8% interest, compounded quaterly, find the future value of this investment

a) after 2 year. b) after 10 years.

4).if $9000 is invested in an account that pays 8% interest, compounded quaterly . find the future value of this investment

a) after 0.5 year b)after 15 years

5. Grandparents decide to put a lump sum of money into a trust fund on their gtanddaughters 10th birthday so that she will have $1000000 on her 60th birthday. if the fund pays 11% compounded monthly. how much money must they put in the account.

6.At the end of t years the future value of an investment of $25000 in an account that pays 12% compounded quaterly is

S=25000(1+0.12 /4t )^4t dollars.. a) How many years will the investment amount to $60000.

a) Calculate the maximum MaxDisk value of the function f (x,y) = 9 ln * (x^2+(1+1)y^2+(0.5+0.5)) on the circle disk with the center of origin and radius 4.

b) Also calculate the maximum the value MaxBorder that the function assumes on the border.

1) Find the velocity and position vectors of a particle that has the given acceleration and the given initial velocity and position.

a(t) = 7i+ 4j,    v(0) = k,    r(0) = i

2) Find the tangential and normal components of the acceleration vector.

r(t) = 5(3t − t³) i + 15t² j

1. Given parametric equations below, find the values of t where the the parametric curve has a horizontal and vertical tangents.

a) x=t^2 - t, y= t^2 + t

b) x= e^(t/10)cos(t), y= e^(t/10)sin(t)

2. Find the arc length of the graph of the parametric equations on the given intervals.

a) x= 4t+2, y = 1-3t , −1 ≤ t ≤ 1

b) x= e^(t/10)cos(t), y= e^(t/10)sin(t), 0 ≤ t ≤ 2π

1. Given parametric equations below, find dy/dx , equations of the tangent and normal line at the given point.

(a) x = t^2 , y = t^3−3t at t = 1

(b) x = cos(t), y = sin(2t) at t = π/4

2. ) Given parametric equations below, find d^2y/dx^2 and determine the intervals on which the graph of the curve is concave up or concave down.

(a) x = t^2 , y = t^3−3t

(b) x = cos(t), y = sin(2t)

Find the equation of the circle ((x-a)² + (y-b)² = r² ) that goes through the points (1, 1), (0, 2), and (3, 2).  [Hint: subtract equations.]

The following DEs are not solvable as written. Perform the given variable change to turn them into something that you are equipped to solve (e.g. either linear, separable or exact) and then find the general solution. Your answer should be in the form y(x)=...y(x)=...

a) dydx=x2+y2−2xydydx=x2+y2−2xy using u=y−xu=y−x

b) xdydx−y=x2−y2−−−−−−√x>0xdydx−y=x2−y2x>0 using u=yxu=yx

c) dydx=y(xy3−1)dydx=y(xy3−1) using u=1y3

Consider the function below.

f(x) =

Find the interval(s) where the function is decreasing. (Enter your answer using interval notation. If an answer does not exist, enter DNE.)

Find the local maximum and minimum values. (If an answer does not exist, enter DNE.)

Find the inflection point. (If an answer does not exist, enter DNE.)

Consider the function below.

f(x) =

Find the interval(s) where the function is increasing. (Enter your answer using interval notation. If an answer does not exist, enter DNE.)

Find the inflection point. (If an answer does not exist, enter DNE.)

local minimum value

Solve the inequality. (Enter your answer using interval notation.)

(x + 5)²(x + 2)(x − 1) > 0