If Pn denotes the predicted number of speeding tickets during the year 2012 + n, then Write the recursive formula for Pn Pn = x Pn-1 Write the explicit formula for Pn Pn = If this trend continues, how many speeding tickets are predicted to be issued in 2029? tickets
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
Having an issue with this problem
![**Exponential Growth of Speeding Tickets in Middletown**
Starting in the year 2012, the number of speeding tickets issued each year in Middletown is predicted to grow according to an exponential growth model. During the year 2012, Middletown issued 160 speeding tickets \( (P_0 = 160) \). Every year thereafter, the number of speeding tickets issued is predicted to grow by 10%.
If \( P_n \) denotes the predicted number of speeding tickets during the year 2012 + n, then:
### Recursive Formula
The recursive formula for \( P_n \) can be expressed as:
\[ P_n = \boxed{1.1} \times P_{n-1} \]
### Explicit Formula
The explicit formula for \( P_n \) can be written as:
\[ P_n = \boxed{160 \times (1.1)^n} \]
### Prediction for the Year 2029
If this trend continues, the number of speeding tickets predicted to be issued in 2029 can be found by substituting \( n \) with 17 (since 2029 is 17 years after 2012) into the explicit formula. Calculate the number of tickets:
\[ \text{tickets} = \boxed{800} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd10f884b-6753-44fe-997f-af50a8e0d0d1%2F7d71a8c6-35e1-45f4-98ae-1567fbd21758%2F5qmx589.png&w=3840&q=75)
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
