8. The population of a community (in millions) can be approximated by $$ p(t)=38.3 e^{x \ln 1.024} $$, where $$ t $$ is years after 2000 . a. What is the estimated population for the year 2030 ? 78.018 Million of people

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To estimate the population for the year 2030 using the given formula $$ p(t) = 38.3 e^{t \ln 1.024} $$, we first need to determine the value of $$ t $$ for the year 2030.

Since $$ t $$ represents the number of years after 2000, for the year 2030:

$$
t = 2030 - 2000 = 30
$$

Now we can substitute $$ t = 30 $$ into the population formula:

$$
p(30) = 38.3 e^{30 \ln 1.024}
$$

Using the property of exponents, we can simplify $$ e^{30 \ln 1.024} $$ to $$ (1.024)^{30} $$:

$$
p(30) = 38.3 \times (1.024)^{30}
$$

Now we need to calculate $$ (1.024)^{30} $$:

$$
(1.024)^{30} \approx 2.030857
$$

Now we can calculate the population:

$$
p(30) \approx 38.3 \times 2.030857 \approx 77.8
$$

So, the estimated population for the year 2030 is approximately **77.8 million** people.

It seems there was a slight discrepancy in your provided answer of 78.018 million; the calculation yields approximately 77.8 million. However, rounding and slight variations in calculations can lead to small differences.
The estimated population for 2030 is approximately 77.8 million people.

The population of a community (in millions) can be approximated by
, where is years after 2000 .
a. What is the estimated population for the year 2030 ?
78.018 Million of people

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The population of a community (in millions) can be approximated by , where is years after 2000 . a. What is the estimated population for the year 2030 ? 78.018 Million of people