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A business with an original capital of ​$40 comma 000 has income and expenses each week of ​$8000 and ​$4700​, respectively. If all profits are retained in the​ business, express the value V of the business at the end of t weeks as a function of t.

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Answer:

V(t) = $40,000 + $3,300t

Step-by-step explanation:

The original capital, or the value V at t = 0, is $40,000.

The change in value per week is given by the difference between weekly income ($8,000) and expenses ($4,700).

Therefore, the value of the business (V) as a function of time 't', in weeks, is described by the following function:

[tex]V(t) = \$40,000+(\$8,000-\$4,700)t\\V(t) = \$40,000+\$3,300t[/tex]

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