High School

The distance, in feet, traveled by a bike is given by the function [tex]d(t) = 7.8t + 28[/tex], where [tex]t[/tex] is measured in seconds. Find and interpret [tex]d(7)[/tex].

A. [tex]d(7) = 82.6[/tex]; after 7 seconds, the bike traveled 82.6 feet.
B. [tex]d(7) = 35.8[/tex]; after 7 seconds, the bike traveled 35.8 feet.
C. [tex]d(7) = 82.6[/tex]; after 82.6 seconds, the bike had traveled 7 feet.
D. [tex]d(7) = 35.8[/tex]; after 35.8 seconds, the bike had traveled 7 feet.

Answer :

After substituting t = 7 in the given function, we find that d(7) = 82.6. This means that after 7 seconds, the bike has traveled 82.6 feet. Therefore, the correct answer is: A. d(7) = 82.6; after 7 seconds, the bike traveled 82.6 feet.

To find d(7), we substitute t = 7 into the function d(t) = 7.8t + 28:

[tex]\[ d(7) = 7.8(7) + 28 \][/tex]

[tex]\[ d(7) = 54.6 + 28 \][/tex]

[tex]\[ d(7) = 82.6 \][/tex]

So, the correct interpretation is: [tex]\[ d(7) = 82.6; \text{ after 7 seconds, the bike traveled 82.6 feet} \][/tex]

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