A house purchased for $250,000 in 2010 increases in value by $10,500 each year. a. Express the value of the house as a linear function of t, the number of years after its purchase. b. According to your function, when will the price of the house reach $334,000?
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.
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![### Problem 20
A house purchased for $250,000 in 2010 increases in value by $10,500 each year.
#### a. Express the value of the house as a linear function of \( t \), the number of years after its purchase.
To express the value of the house as a linear function of \( t \), we can use the formula for a linear function:
\[ V(t) = mt + b \]
where:
- \( V(t) \) is the value of the house at time \( t \),
- \( m \) is the rate of increase in value per year,
- \( t \) is the number of years after the house was purchased,
- \( b \) is the initial value of the house.
Given:
- Initial value \( b = 250,000 \),
- Annual increase \( m = 10,500 \).
So, the linear function is:
\[ V(t) = 10,500t + 250,000 \]
#### b. According to your function, when will the price of the house reach $334,000?
To find out when the price will reach $334,000, we need to solve for \( t \) in the equation:
\[ V(t) = 334,000 \]
Using the linear function from part (a):
\[ 334,000 = 10,500t + 250,000 \]
Subtract 250,000 from both sides:
\[ 334,000 - 250,000 = 10,500t \]
\[ 84,000 = 10,500t \]
Now, solve for \( t \):
\[ t = \frac{84,000}{10,500} \]
\[ t = 8 \]
So, the price of the house will reach $334,000 in 8 years after its purchase, which will be in 2018.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff8ec627b-d95d-4a8e-b0e9-8b769944a253%2Fadd641cd-6446-48b4-9031-e9f49dfaed79%2F0s9nt8_processed.png&w=3840&q=75)
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