1)A frog hops out of a pool of radioactive goo. the scientists discover that the frog registers 10 curies of radioactivity initially and that three days later it registers 7 curies of radioactivity. when will its level of radioactivity reach 2 curies. this is exponential decay

2)at noon, a truck heads north from an intersection at a constant speed of 60 miles per hour. there is a house 100 miles to the west of the intersection. how fast is the distance between the truck and house changing by 3pm? no need to simplify answer

3)compute the value of the riemann sum for the function f(x)=(2x+1) on the interval [1,4] using n=3 and taking the left endpoint. leave answer as sum of square root

4)a closed box with square base is to be built to house an ant colony. the bottom of the box and all four sides are to be made of materials costing $1/ft^2, and the top, is to be constructed of glass costing $5/ft^2. what are the dimensions of the box of greatest volume that can be constructed for $72.

5)the marginal revenue of a certain product is R'(x)=3x^2+2x. if the revenue from selling 3 items is $10, what is the revenue from selling 10 items.

6)the marginal revenue of a certain commodity is R'(x)=-3x^2+4x+32 where x is the level of production in thousands. assume R(0)=0. find the level of production that maximizes revenue.

7)if f(x) = x if x<1

1/x if x1

find f(t)dt on [0,5]

8) a particle travels along at the x-axis in such a way that its acceleration at time t is a(t)=(t) +t^2. if it starts at the origin with an initial velocity of 2 (that is, s(0)=0 and v(0)=2) determine its position and velocity when t=1. don't need to simplify.

9) if 1200 square centimeters of material is available to make a box with a square base and an open top, find the largest possible volume of the box. the surface area should be 1200 square centimeters

10)a tinsmith wants to make an open topped box out of a rectangular sheet of tin 3 in wide 8in long. the tinsmith plans to cut congruent squares out of each corner of the sheet and then bend and solder the edges of the sheet upward to form the sides of the box. for what value of x does the box have the greatest possible volume.

11)suppose that s=(16/15) (^3)(r^6). if there is an error of 3 percent in the measurement of r, approx. what percentage error should be expected in the computation of s.