Answer: Option D.
Explanation:
An exponential function is something like:
f(x) = A*(r)^x
Where:
A = initial amount.
r = rate of growth
x = variable.
This type of function is used to describe situations like "you have A dollars, and it increases by 30% each week"
or:
"There is a population of A animals, and it doubles each year"
Let's analyze briefly all the given options and see which one is an exponential function.
A) The water level of a tank decreases by 5 gallons every day.
This is a linear relation, if W is the initial amount of water, and x is the number of days, then the water level of the tank after x days is:
y = W - 5 gal*x
B) The amount of money collected by a charity increases by $5,000 each year.
The amount collected increases $5000 each year.
Then if in year 1 they collected A.
in year 2 they collected A + $5000
in year 3 they collected A + 2*$5000
We already can see the pattern, this is a linear relation:
in year X they colected A + (X - 1)*$5000
C) A tree was 10 feet tall when purchased and grows at a rate of 2 feet per year.
if y is the height of the tree, and x is the number of years, this can be written as:
y = 10ft + x*2ft
Again, a linear relation.
D) The number of people in a stadium is decreasing at a rate of 45% every 10 minutes.
Let's define x as each "lapse" of 10 minutes that passes.
If N is the initial number of people in te stadium, then after 10 minutes the number of people is = N*(1 - 45%/100%) = N*(1 - 0.45) = N*0.55
After another 10 minutes, the population decreases again.
N*0.55*(1 - 45%/100%) = N*0.55*0.55 = N*0.55^2
We can see the pattern here, this can be written as
People(x) = N*(0.55)^x
This is an exponential function.