Question

How do you write a function of t that represents the situation(sales $10,000 increase by 65% each year)?

Answer 1

Answer:

  s(t) = 10000·1.65^t

Step-by-step explanation:

The general form of an exponential model is ...

  f(t) = (initial value) × (1 +(fractional change))^t

where the fractional change can be positive or negative and t is the number of time units. Each time unit will correspond to the period required for the fractional change.*

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For your problem, you have (initial value) = 10,000 and (fractional change) = 65% = 0.65 with time units of 1 year. Your function for sales (s) will then be ...

  s(t) = 10000·1.65^t

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* The business regarding time units has to do with problems where you get a description like "increased 30% in 4 hours." Then, if t is in hours, the multiplier of the initial value looks like 1.30^(t/4).