Pam and Jim were peeling potatoes for dinner. Pam peels 5 potatoes every minute and Jim can peel 3 potatoes per minute. Jim gets a 4-minute head start, and then they continue peeling together until they have finished the pile. If they each peel the same number of potatoes, how many potatoes were there when they started?

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.

so, converting firstly the mixed fractions to improper fractions and then "adding".

$79500

step-by-step explanation: