How do you multiply mixed numbers the easy way?
2 answers:
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Answer:
The rate at which the total personal income was rising in the Richmond-Petersburg area in 1999 is $1.627 billion per year
Step-by-step explanation:
Let be the number of years after 1999.
From the information given:
- In 1999, the population in this area was 961400, and the population was increasing at roughly 9200 people per year.
- The average annual income was 30593 dollars per capita, and this average was increasing at about 1400 dollars per year.
The population growth can be modeled with a linear equation. The initial population was is 961400 and it grows by 9200 people per year.
The population in time t can be written
The average annual income can be modeled with a linear equation. The initial average annual income was 30593 dollars per capita and it grows by 1400 dollars per year.
If we multiply both together gives the total personal income at time t.
The rate at which the total personal income was rising in the Richmond-Petersburg area is the derivative
We need to use the Product Rule that says
If f and g are both differentiable, then:
Applying the Product Rule
For 1999, t = 0.
The raising is
The rate at which the total personal income was rising in the Richmond-Petersburg area in 1999 is $1.627 billion per year.