Answer:
34175 people will live in Pattersonville 8 years from now
Step-by-step explanation:
Initial population of Pattersonville =40,500
We are given that The census indicated that the population of the town has been decreasing by 2.1% per year .
Now we are supposed to find If this trend continues , approximately how many people will live in Pattersonville 8 years from now
Formula : 
Where N(t)= Population after t years
= Initial population
r = rate of decrease = 2.1 %=0.021
t = 8 years
Substitute the values in the formula :
So,
N(8)=34175.63223
So, 34175 people will live in Pattersonville 8 years from now
Answer:
3.56*10^13
Step-by-step explanation:
8.9* 10^4 * 4*10^8
Multiply the number out front and then the exponents
8.9 * 4 * 10^4 * 10^8
When we multiply powers when the bases are the same, we add the exponents
35.6 * 10^(4+8)
35.6 *10^12
But this is not in proper scientific notation. Only one digit before the decimal
Move the decimal one place to the left, that means we need to add 1 to the exponent
3.56 *10^(12+1)
3.56 * 10^13
Answer:
Step-by-step explanation:
There are exponent rules I posted above that are being used here.
We have (3^-6)^-5
Since we have a power times a power, we multiply 6 and 5 to get -30. Look at the first example in the photo.
So, we're left with 3^-30.
If you look at the photo, there's a rule for negative exponents.
Take the inverse of the base number, so 3 in this case:
1 / 3
and then make the exponent positive after taking the inverse.
So, we should get 1 / 3^30
Hope this helps!
1.
"The spending limit on John’s credit card is given by the function f(x)=15,000+1.5x"
means that if the monthly income of John is $ 5,000 ,he can spend at most
f(5,000)=15,000+1.5*5,000=15,000+ 7,500=22, 500 (dollars)
Or for example
if Johns monthly income is $8,000, then he can spend at most
f(8,000)=15,000+1.5*8,000=15,000+ 12,000=27,000 (dollars)
2.
Now, assume that the maximum amount that John can spend is y.
Then, y=15,000+1.5x
we can express x, the monthly income, in terms of y by isolating x:
y=15,000+1.5x
1.5x = y-15,000
X=y-15,000/1.5
thus, in functional notation, x, the monthly income, is a function , say g, of variable y, the max amount:
X=g(y) y-15000/1.5
since we generally use the letter x for the variable of a function, we write g again as:
G (x) x-15000/1.5
tells us that if the maximum amount that John can spend is 50,000 $, then his monthly income is 23,333 $.
3.
If John's limit is $60,000, his monthly income is
G(600,000)=60,000-15,000/ 1.5=45,000/1.5 =30,000
dollars.
Answer: $ 30,000
Remark: g is called the inverse function of f, since it undoes what f does.
instead of g(x), we could use the notation
