QuestionThe number of households in a local school district has been increasing linearly over the last ten years. In 2010, there were 985 households, and in 2020 there were 1579 households.
Question 3/10
Let H represent the number of households at $t$ represent the number of years since 2010. The linear model for the number of households in the school district is $H=59.4 t+985$
Use the linear model to predict the number of households in 2025.

Studdy Solution

STEP 1

1. The number of households has been increasing linearly.
2. In 2010, there were 985 households.
3. In 2020, there were 1579 households.
4. The linear model for the number of households is given by $H = 59.4t + 985$ .
5. We need to predict the number of households in 2025.

STEP 2

1. Determine the value of $t$ for the year 2025.
2. Substitute the value of $t$ into the linear model.
3. Calculate the predicted number of households.

STEP 3

Determine the value of $t$ for the year 2025.
Since $t$ represents the number of years since 2010, for the year 2025:
$t = 2025 - 2010 = 15$

STEP 4

Substitute the value of $t$ into the linear model.
The linear model is given by:
$H = 59.4t + 985$
Substitute $t = 15$ into the equation:
$H = 59.4 \times 15 + 985$

STEP 5

Calculate the predicted number of households.
First, calculate $59.4 \times 15$ :
$59.4 \times 15 = 891$
Now, add 985 to the result:
$H = 891 + 985$ $H = 1876$
The predicted number of households in 2025 is:
$\boxed{1876}$

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