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It is given that in 2013, McDonald's had 14267 locations in the US. It is also given that the population of the US was approximately 316.5 million citizens in 2013. Now, we know that 316.5 million=316500000.
Therefore, in order to find the number of McDonald's restaurants per capita in the US in 2013 all that we have to do is divide the number of McDonald's restaurants in 2013 with the population of the same year.
Thus, we get, number of McDonald's restaurants per capita in the US in 2013 to be:
(the answer has been expressed in scientific notation rounded correctly to three decimal) places.
Answer:
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Step-by-step explanation:
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Answer:
f(t) = -t + 21
g(t) = 18*e^( - t / 12 + 1/4 )
Step-by-step explanation:
Given:
- The graphs for the similar question is attached.
- The same graph would be used as reference but with different coordinates for point of intersection of f(t) and g(t) @ ( 3 , 18 ) & ( 15 , 6 ).
Find:
- The formulas for functions f(t) and g(t).
Solution:
- First we will determine f(t) the blue graph which is a "linear" function. The general equation for the linear function is given as:
f(t) = m*t + c
Where, m: is the gradient ( constant )
c: The f(t) intercept. ( constant )
- The gradient m can be determined by the given points that lie on the graph:
m = ( f(t2) - f(t1) ) / ( t2 - t1 )
m = ( 6 - 18 ) / ( 15 - 3 )
m = -12 / 12 = -1
- The constant c can be evaluated by using any one point and m substituted back into the linear expression as follows:
f(t) = -t + c
18 = -(3) + c
c = 21
- The function f(t) is as follows:
f(t) = -t + 21
- The general expression for an exponential function can be written as:
g(t) = a*e^(b*t)
Where, a and b are constants to be evaluated.
- We will develop two expressions for g(t) using two given points that lie on the curve as follows:
18 = a*e^(3*b)
6 = a*e^(15*b)
- Divide the two expressions we have:
3 = e^( 3b - 15b )
Ln(3) = -12*b
b = - Ln(3) / 12
- Then the expression 1 becomes:
18 = a*e^( - Ln(3)*3 / 12)
18 = 3*a*e^(-1/4)
6 = a / e^(0.25)
a = 6*e^( 1 / 4 )
- The function g(t) can be expressed as:
g(t) = 18*e^( - t / 12 + 1/4 )
