A study of the annual population of butterflies in the country park shows the population, B(t), can be represented by the function B(t)=137(1.085)^t, where the T represents the number of years since the study started based on the function what is the growth rate

Given:

Annual population of butterflies after t years is

To find:

The growth rate.

Solution:

The general exponential function is

       ...(i)

where, a is initial value, t is time and r is growth rate.

We have,

It can be written as

          ...(ii)

On comparing (i) and (ii), we get

Initial value :

Growth rate :

Therefore, the growth rate is 8.5%.

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200.   after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes           1800 - 6400 which gets you 11,600.

2/3

step-by-step explanation: