12 Suppose that the model which describes the relationship between the literacy rate of a country and the GDP of that country can be modelled by the equation:
literacy rate
From this model we would predict that a country with a GDP of would have a literacy rate of:

A
B
C
D
E

13 Suppose that the relationship between the amount of money (in $million) won by a tennis player ranked in the top 25 and their ranking can be modelled by the equation:

From this model we would predict that a player ranked at number 10 would win approximately:

A million
B million
C million
D million
million

Ask by Gough Coleman. in Australia

Mar 27,2025

Question

12 Suppose that the model which describes the relationship between the literacy rate of a country and the GDP of that country can be modelled by the equation:
literacy rate
From this model we would predict that a country with a GDP of would have a literacy rate of:

A
B
C
D
E

13 Suppose that the relationship between the amount of money (in $million) won by a tennis player ranked in the top 25 and their ranking can be modelled by the equation:

From this model we would predict that a player ranked at number 10 would win approximately:

A million
B million
C million
D million
million

Ask by Gough Coleman. in Australia

Mar 27,2025

UpStudy AI · Accepted Answer

**12. Calculation for Literacy Rate**

We are given the equation  
$$
\text{literacy rate} = -40 + 30 \times \log(\text{GDP})
$$

For a country with a GDP of $$ \$20000 $$, we plug in:
$$
\log(20000) = \log(2 \times 10^4) = \log(2) + \log(10^4) = \log(2) + 4.
$$
Using base 10 logarithms, we know that $$\log(2) \approx 0.3010$$. Thus,
$$
\log(20000) \approx 0.3010 + 4 = 4.3010.
$$

Now substitute into the model:
$$
\text{literacy rate} \approx -40 + 30 \times 4.3010.
$$
$$
30 \times 4.3010 = 129.03.
$$
Thus,
$$
\text{literacy rate} \approx -40 + 129.03 = 89.03\%.
$$

The predicted literacy rate is about $$89\%$$, which corresponds to option **A**.

---

**13. Calculation for Tennis Player's Winnings**

We are given the equation  
$$
\text{winnings} = 0.491 + 5.767 \times \frac{1}{\text{rank}},
$$
where the winnings are in millions of dollars.

For a player ranked $$10$$, we have:
$$
\frac{1}{\text{rank}} = \frac{1}{10} = 0.1.
$$

Substitute into the model:
$$
\text{winnings} = 0.491 + 5.767 \times 0.1.
$$
$$
5.767 \times 0.1 = 0.5767.
$$
$$
\text{winnings} \approx 0.491 + 0.5767 = 1.0677 \text{ million dollars}.
$$

This is approximately $$\$1.068$$ million, corresponding to option **E**.
**12. Literacy Rate Prediction** For a GDP of \$20,000, the predicted literacy rate is approximately **89%**. **13. Tennis Player's Winnings** A player ranked 10th would win approximately **\$1.068 million**.

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