The rate of auto thefts triples every 9 months. (a) Determine, to two decimal places, the base b for an exponential model y = Abt of the rate of auto thefts as a function of time in months. HINT [See Section 2.2 Example 2.] b = (b) Find the doubling time to the nearest tenth of a month. Incorrect: Your answer is incorrect. months

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

5   1/4   miles per hour

step-by-step explanation:

15   3/4 / 3 = 5   1/4