A circle's radius that has an initial radius of 0 cm is increasing at a constant rate of 7 cm per second. Write a formula to expresses the radius of the circle, r (in cm), in terms of the number of seconds, t , since the circle started growing.

r = 7t

or not mathematically,

r(t) = 7t

r(t) means, r, which is a function of t.

Step-by-step explanation:

Initial size of the radius = 0 cm, at t = 0 s

Rate of increase of the radius of the circle = 7 cm/s

dr/dt = 7

dr = 7 dt

∫ dr = 7 ∫ dt

r = 7t + C (C is the constant of integration)

At t = 0, r = 0,

0 = 0 + C

C = 0

r = 7t.

r(t) = 7t

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.

366

step-by-step explanation: