29. Copper production increased at a rate of about $$ 4.9 \% $$ per year between 1988 and 1993 . In 1993 , copper production was approximately 1.801 billion kilograms. If this trend continued, which is the best model of copper production (P), in billions of kg , since 1993 ? $$ \begin{array}{ll} ext { a) } p=1.801(4.900)^{t} & ext { b) } p=1.801(1.490)^{t} \ \begin{array}{ll} ext { c) } p=1.801(1.049)^{t} & ext { d) } p=1.801(0.049)^{t}\end{array}\end{array} \begin{array}{l} ext { A }\end{array} $$

Question

29. Copper production increased at a rate of about $$ 4.9 \% $$ per year between 1988 and 1993 . In 1993 , copper production was approximately 1.801 billion kilograms. If this trend continued, which is the best model of copper production (P), in billions of kg , since 1993 ? $$ \begin{array}{ll}	ext { a) } p=1.801(4.900)^{t} & 	ext { b) } p=1.801(1.490)^{t} \ \begin{array}{ll}	ext { c) } p=1.801(1.049)^{t} & 	ext { d) } p=1.801(0.049)^{t}\end{array}\end{array} \begin{array}{l}	ext { A }\end{array} $$

UpStudy AI · Accepted Answer

To model the copper production growth accurately, we'll use the exponential growth formula:

$$
P(t) = P_0 \times (1 + r)^t
$$

Where:
- $$ P(t) $$ is the copper production after $$ t $$ years.
- $$ P_0 $$ is the initial production.
- $$ r $$ is the annual growth rate.
- $$ t $$ is the time in years since the initial measurement.

**Given:**
- Initial production in 1993, $$ P_0 = 1.801 $$ billion kg.
- Annual growth rate, $$ r = 4.9\% = 0.049 $$.

Plugging these values into the formula:

$$
P(t) = 1.801 \times (1 + 0.049)^t = 1.801 \times (1.049)^t
$$

**Analyzing the Options:**
- **Option a:** $$ P = 1.801 \times (4.900)^t $$  
  - Incorrect base. A growth rate of 4.9% should be represented as 1.049, not 4.900.

- **Option b:** $$ P = 1.801 \times (1.490)^t $$  
  - Incorrect base. This suggests a 49% growth rate, which is much higher than the given 4.9%.

- **Option c:** $$ P = 1.801 \times (1.049)^t $$  
  - **Correct.** This accurately represents a 4.9% annual growth rate.

- **Option d:** $$ P = 1.801 \times (0.049)^t $$  
  - Incorrect base. This implies a dramatic decrease rather than growth.

**Conclusion:**
The best model for copper production since 1993, considering a 4.9% annual growth rate, is:

$$
\boxed{\text{c) } p=1.801(1.049)^{t}}
$$
The best model for copper production since 1993 is $$ p = 1.801 \times (1.049)^t $$.

Copper production increased at a rate of about per
year between 1988 and 1993 . In 1993 , copper production was
approximately 1.801 billion kilograms. If this trend continued,
which is the best model of copper production §, in billions of
kg , since 1993 ?

Upstudy AI Solution

Answer

Solution

The Deep Dive

Related Questions

Latest Pre Calculus Questions

Copper production increased at a rate of about per year between 1988 and 1993 . In 1993 , copper production was approximately 1.801 billion kilograms. If this trend continued, which is the best model of copper production §, in billions of kg , since 1993 ?