Question

what base could be written in the blank to make the exponential function model 15% decay ? y= (____) ^t\12

Answer 1

For this case we have a function of the form:
 $y = A * (b) ^ t$
 Where,
 A: it is the initial amount
 b: decrease rate (b <1)
 t: time (years, months, days)
 We have the following function:
 $y = (b) ^ {( \frac{1}{12} t)}$
 The value of base b is:
 $b = (100-15) / (100) b = 0.85$
 The function is:
 $y = (0.85) ^ {( \frac{1}{12} t)}$
 Answer:
 the base of the function is:
 $b = 0.85$