Consider the sphere, x^2 + y^2 + z^2 = 2, and the paraboloid z = x^2 + y^2. Requried:
a. Describe the intersection of the sphere and the paraboloid in terms of a pair of equations.
b. Write down the iterated triple integral in cylindrical coordinates that represents the volume of the region bounded above by the sphere and below by the paraboloid. Hence evaluate this volume.
c. Write down the iterated triple integral in spherical coordinates that represents the volume of the region defined in (b). Do not evaluate this integral.

linearly: 8560 bacteria

exponentially: approximately 75233 bacteria

step-by-step explanation:

assuming it is not exponential (we would have some really complicated logarithms), let's say it is linear. then, after 5 hours, it increased by 1200 bacteria, so every hour it increases by 240 bacteria. this means that after 19 hours, we get 19 * 240 + 4000 bacteria or 3800 + 760 + 4000 = 7800 + 760 = 8560 bacteria.

because it says round your answer, i will do this exponentially (with a calculator, of course). first, we need to find how much it multiplies by every hour, by taking the 5th root of 52/40 or 13/10. this is approximately 0.167. we still need to add 1 to this, because we are multiplying by that number, not adding that amount of the number. now, we just calculate 4000 * (1.167)^19. use a calculator to get approximately 75232.6, or 75233.

step-by-step explanation: