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  a)  f(t) = 8000(1.015^t)

Step-by-step explanation:

The growth factor is 1 more than the growth rate. Here, the growth rate is 1.5%, so the growth factor is 1 + 0.015 = 1.015. This is the base of the exponential term. Each year that passes causes the balance to be multiplied by this factor, so the exponent is the number of passing years.

  f(t) = 8000(1.015^t)

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation: