10. 80 machines can produce 4800 identical pens in 5 hours. At this rate a) how many pens would one machine produce in one hour?
b) how many pens would 25 machines produce in 7 hours?

12 and 2100

Step-by-step explanation:

(a)

Divide 4800 by 5 for pens per hour produced by 80 machines.

4800 ÷ 5 = 960 pens per hour

Divide 960 by 80 for pens per hour produced by 1 machine.

960 ÷ 80 = 12

Thus 1 machine produces 12 pens per hour

(b)

Multiply 12 by 7 for pens produce in 7 hours by 1 machine.

12 × 7 = 84 pens per hour

Multiply 84 by 25 for pens produced in 1 hour by 25 machines.

84 × 25 = 2100

Thus 2100 pens are produced by 25 machines in 1 hour

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.