Answer:
a) b ≈ 1.13
Step-by-step explanation:
The rate of auto thefts triples every 9 months.
(a) Determine, to two decimal places, the base b for an exponential model y = Ab^t of the rate of auto thefts as a function of time in months.
A = rate of auto thefts when t = 0
We are told the rate of auto thefts triple every 9 months. Hence,
3A = Ab⁹
We divide both sides by A
3A/A = Ab⁹/A
3 = b⁹
Raise both to the power of 1/9
3^⅑ = b⁹ × ⅑
b = 1.1298309639
Approximately to two decimal places
b ≈ 1.13
(b) Find the doubling time to the nearest tenth of a month.
y = Ab^t
y = 2A, b = 1.13
2A = A(1.13)^t
Divide both sides by A
2A/A = A(1.13)^t/A
2 = (1.13)^t
t = In 2/In 1.13
t = 0.6931471806/0.1222176327
t = 5.6714171702
Approximately to the nearest tenth of a month, the doubling time 5.7 months
