Answer:
F(10) = 14.41 Billion
The total number of hamburgers that will have been sold by 2013 is 14.41 billion.
Explanation:
The exponential function representing the total number of hamburgers sold by a national fast-food chain which grows exponentially can be expressed as;
f(t) = p(a)^t
In 2003, t = 0 and f(0) = 3 Billion
f(0) = p = 3 billion
The initial value p = 3 billion
In 2010, t = (2010-2003) = 7
f(7) = p(a)^7 = 9 billion
3(a)^7 = 9
a^7 = 9/3 = 3
a = 3^(1/7)
Therefore, the function f(t) is;
f(t) = 3(3)^(t/7) .......2
In 2013, t = (2013 - 2003) = 10
Substituting t = 10 into equation 2;
f(10) = 3(3)^(10/7)
F(10) = 14.41195997001 Billion
F(10) = 14.41 Billion
The total number of hamburgers that will have been sold by 2013 is 14.41 billion.