The average births per woman in a certain developing country can be modeled according to the equation f(x)=0.006x2−0.35x+7.06f(x)=0.006x2−0.35x+7.06 where x is the number of years since 1956.

Step 1 of 2 :

What was the average births per woman in the country in 1992?

To find the average number of births per woman in the country in 1992, we can substitute the year 1992 into the given equation. First, determine the value of \( x \), where \( x \) is the number of years since 1956:

\[
x = 1992 - 1956 = 36
\]

Now, substitute \( x = 36 \) into the equation \( f(x) = 0.006x^2 - 0.35x + 7.06 \):

\[
f(36) = 0.006(36)^2 - 0.35(36) + 7.06
\]

We can now compute this:

\[
f(36) = 0.006(1296) - 0.35(36) + 7.06
\]

\[
f(36) = 7.776 - 12.6 + 7.06
\]

\[
f(36) = 2.236
\]

So, the average births per woman in the country in 1992 was approximately **2.236**.

Would you like more details on this, or do you have any questions?

### 5 Related Questions:
1. How does the equation change as the number of years increases?
2. What does the coefficient of \( x^2 \) indicate about the trend in births per woman?
3. How would the average births per woman in 1980 be calculated?
4. How does the average number of births change over time according to this model?
5. How would you interpret the significance of the constant \( 7.06 \) in this equation?

### Tip:
When dealing with quadratic models, the term \( x^2 \) typically indicates a non-linear trend, often showing an increase or decrease at an accelerating or decelerating rate.

What was the average births per woman in the country in 1992? The average births per woman in a certain developing country can be modeled according to the equation f(x)=0.006x^2−0.35x+7.06 where x is the number of years since 1956.

Discover how to calculate the average births per woman in a developing country in 1992 using the quadratic function f(x) = 0.006x^2 − 0.35x + 7.06, where x is the number of years since 1956. Step-by-step solution with detailed explanation of key algebraic concepts, suitable for high school students.

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