Rewrite f(t)=0.4(1.16)^t−1 in the form y=a(1+r)^t or y=a(1−r)t to determine whether it represents exponential growth or decay. Round a and r to the nearest hundredth if necessary.

Answer 1

y = 0.4(1.16)^t-1

Use the exponent property x^a+b = x^ax^b

y = 0.4(1.16)^t(1.16)^-1

Use the exponent property that x^-1 = 1/x

y = (0.4/1.16)·(1.16)^t

y = 0.35·(1+0.16)^t

It is now in the form y = a·(1+r)^t where a = 0.35 (rounded to the nearest hundredth) and r = 0.16.