Math help me please!!!

The animal Eraticus is endangered. Since 1995 there has only been one colony remaining and in 1995 the population of the colony was 555. Since then the population has been steadily decreasing at 4.5 % per year.
Find:
a)the expected population in the year 2010.
b) the year in which we would expect the population to have declined to 50.

OK

1995 to the year 2010 is 15 years. Each year the group is decreasing by 4.5%

555 * (1 - .045)^15 = Expected population in 2010
555 * .955^15 = x
555 * .501 = x
278.19 = x ; since you can't have a fraction of an animal, I would expect the the colony would be 278 in the year 2010.

To do the second part, change the equation slightly to get the variable you need - like this:

555 * (1 - .045)^ x = 50
.955^x = 50/555
.955^x = .09
x = 52.2748 , which is sightly more than 52 and 1/4 years. So the population would be expected to fo to 50 in 1995 +52 = 2047.

Hope that helps.

the equation for exponential decrease for a) is
y = 555(1 - .045)^(15)
y = p(1-r)^t
t is the number of years since 1995 which is 15.
Now, solve for y - you'll need a calculator
First do the 1 - .045, then raise that to the 15th power then multiply by 555

Now for part b). Same equation different variable.
50 = 555(1 - .045) ^t
To solve for t, you can use trial and error or you can use logarithms
Again, you'll need a calculator.
50/555 = .955^t
.090909 = .955^t
log .090909 = t log .955
t = (log .090909)/(log .955)
Once you find t, that will tell you how many years it will take for the population to decrease to 50. You will have to add that number of years to 1995 to find out what year it will be when that occurs.
Good luck

Intuition:
In 1995 the population was 555. 4.5% of these died, 4.5% of 555 = 25, so in 1996 there were 555-25=530. Then in 1996 4.5% of these died, 4.5% of 530 = 23.85 and in 1997 there were 530-23.85=506 and so on...