In a laboratory the countof bacteria in a certain experiment was increasing at the rate of 5% per hour find the bacteria at the end of 3 hour if the count was initially 25?

289,406.25 ≈ 289,406

Explanation:

We can solve this question in 2 ways: Simple calculation and Using the formula.

Simple Calculation: The rate of increase is 5% per hour. And the initial count was 250,000. Therefore, in the first hour, the increase in the count would be 5% of 250,00, which is ×250,000 = 12,500. Therefore,  at the end of the first hour, the count would be 250,000 + 12500 = 262,500. Now, for the 2nd hour, the intial count is 262,500 and the increase in count at the end of the 2nd hour would be 5% of 262,500 = ×262,500 = 13,125. And the count at the end of the 2nd hour is 262,500+13,125 = 275,625. Similarly for the 3rd hour, the starting count is 275,625 and the increase in count at the end of the 3rd hour is ×275,625 = 13,781.25. Thus, the total count at the end of 3rd hour is 275,625+13,781.25 = 289,406.25 ≈ 289,406.

Direct Formula (Actually, it is the compound interest formula): , where C(f) is final count, C(i) is the initial count, r is the rate of increase, n is the number of times rate of increase is applied in a time period, T is the number of time periods. Here, C(i) = 250,000, r is 5% = 0.05, n is one (because 5% increase happens once in one hour) and T is 3 hours.  Therefore, .

the tides are influenced by both the moon and the sun, it's easy to see that when the sun lines up with the moon and the earth, as during a new moon or full moon, the tidal effect is increased. these are known as spring tides, named not for the season, but for the fact that the water "springs" higher than normal. on the other hand, if the sun and the moon are 90 degrees apart in relation to an observer on earth as during the first quarter moon or third quarter moon, then high tides are not as high as they normally would be. this is because despite its greater distance, the sun's mass allows it to exert enough gravitational force on the oceans that it can negate some of the effects of the moon's pull. this phenomenon of lower high tides is called a neap tide. if you need more information on this topic visit moonconnection.com.