Answer A):
s-intercept means y-intercept as s ( number of t-shirts) is graphed along y-axis.
We see that graph crosses y-axis at (0,6)
So that means s-intercept is = (0,6)
s-intercept (0,6) indicates that t-shirts sold in year 2000 is 6 thousand.
t-intercept means x-intercept as t ( year) is graphed along x-axis.
We see that graph doesn't cross x-axis
So that means there is NO t-intercept.
No t-intercept means there was no year after production start when they sold 0 t-shirts.
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Answer B):
From graph we can clearly see that as t increases then f(t) also increases so for the end behavior we will write "increases" in the blank space.
It means as the time increases then sales also increases.
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Answer C):
Average rate of change can be calculated by formula of slope which is:
[tex]ARC=\frac{\left(y_2-y_1\right)}{\left(x_2-x_1\right)}=\frac{\left(12.5-22\right)}{\left(5-7\right)}=\frac{-9.5}{-2}=4.75[/tex]
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Answer D):
Given that g(t) is sum of T-shirts sold online and at the basketball games where sold -shirts in basketball game = 1000 T-shirts. But f(t) is in hundreds so that means 1000 T-shirt will make increment of 10 in value of f(t) hence graph of g(t) will be just 10 unit above than graph of f(t).
Then equation of g(t) will be:
[tex]g(t)=f(t)+10[/tex]
[tex]g(t)=(1.5)^t+5+10[/tex]
[tex]g(t)=(1.5)^t+15[/tex]
Hence final answer is [tex]g(t)=(1.5)^t+15[/tex]
