Calculus Answers

1. A certain radioactive element has a half-life of 5 hours. If its initial mass is at

6,470 grams, how many grams are left after 2 days?

2. Carlo’s online investment is worth Php870,000 on its 3rd year and Php650, 000

on its 7th year. What is the worth of his initial investment?

3. The pressure exerted on us by the atmosphere decreases exponentially as you

go up. The pressure at ground level is 1,013 hPa and decreases to 965 hPa at

381 meters. What is the pressure at the summit of Mt. Apo which is at 2,954

meters?

4. A strain of bacteria growing on the palm of your hands is 9 bacteria after 6

minutes. If you start with only one bacterium and follows an exponential growth

model, how many bacteria could be present at the end of 1 hour?

5. A certain breed of rats doubles its population every 2 months. Assuming there

were only 6 rats initially at a certain area, how many months will it take for the

population to grow to 68 rats?

Compute the area of the plane region bounded by the curve x=y²-2 and the line y=-x using integration along the y-axis.

Consider the R²-R function f defined by f(x,y)=x²+2y²-x²y.

Show that f has two saddle points

Consider the R²-R function f defined by f(x,y)=e^xIn(1+y).

Find the third order Taylor polynomial of f about the point (0,0)

Convert (√3,-1)into polar coordinates (r,0) so that r≥0 and 0≤0<2π

Find implicit differentiation of 2y+cot(xy^2)=3xy

A rock is thrown horizontally from the top of a cliff 88 m high, with a horizontal speed of 25 m/s. with what velocity does the rock hit

Derive an equation x(t) for the instantaneous position of the car as a function of time. Identify the

●      value x when t = 0 s

●      asymptote of this function as t → ∞

t(0-28 m/s) (s) t(400m)(s) t (Maxspeed)(s)

2.5 9.75 8.0

The fixed cost of a company is 35000 and the variable cost per unit is 500 and the revenue function for sale is X units is given by R(x)=5000X-100X²

I) find the profit function

Ii) break even values

III)the values of X which results in a loss

The demand function is Q=280000-400p

Where Q equals the number of units demanded and p equals the price in dollars of the total cost of producing Q units of the product is estimated by the function

C=350000+300q+0.0015q²

I) how many units should Q produce in order to maximize its annual profit

Ii) what price should be charged

III) determine the annual profit expected