2. A kayaker travels 4 miles upstream and 4 miles downstream in a total of 6 hours. In still
water, the kayaker can travel at an average speed of 2.3 mi/h.
Determine the average speed of the river's current.

The average speed of the river's current is 1.49107 miles per hour

Solution:

Given that,

Upstream distance = 4 miles

Downstream distance = 4 miles

If the speed of a boat in still water is u km\hr and the speed of the stream is v km/hr then:

Speed downstream = u + v km\hr

Speed upstream = u - v km\hr

From given,

Speed in still water = 2.3 miles per hour

u = 2.3

Therefore,

speed downstream = 2.3 + v

Speed upstream = 2.3 - v

The total time is 6 hours

Therefore,

Thus we get,

Thus the average speed of the river's current is 1.49107 miles per 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.

a

step-by-step explanation: