Answer:
log(.375)/log(.955) = x
Step-by-step explanation:
To decrease by 4.5% means you multily by 1-.045 or .955. It might be easier to see if you write it as 8000 - 8000 * .045. Either way, now you can write it as 8000*.955.
Now, if this happened again you would multiply by .955 twice, or in other words have 8000 * .955^2. You can keep going with this, which shows you can make this an exponential function. 8000*.955^x where x is the number of years the population decreases by 4.5%
The question then says how many times would we hae to decrease by 4.5% to get to 3000. One way to do this is try every x value until you get there. That usually takes a long time, so instead we use logs.
If you don't understand logs let me know, but basically it takes exponential functions and turns them into something else. specificlaly it takes a = b^x where a and b are just numbers and x is the exponent, and turns it into log_b(a) = x or log base b of a equals x. This will let us solve for x as a variable.
To enter this into a calculator jut use log(a)/log(b) or ln(a)/ln(b).
Anyway, we start with 3000 = 8000*.955^x That's not quite what we need to start with so divide both sides by 8000
3000/8000 = .955^x
3/8 = .955^x
.375 = .955^x
Then turn it into logarithmic form
log_.955(.375) = x
then just solve with the method I showed
log(.375)/log(.955) = x
