Solve.

The population of a particular country was 29 million in 1980; in 1989, it was 36 million. The exponential growth function A=29e^kt describes the population of this country t years after 1980. Use the fact that 9 years after 1980 the population increased by 7 million to find k to three decimal places.

36 = 29 e^(9k)

1.24138 = e^(9k)
9k = ln (1.24138)
k = ln (1.24138)/9
= ....

36M=29M*e^k9

take the ln of each side.
ln(36)=ln29+ 9k
k= (ln(36/29)) /9

Thank you again! Both of u. much appreciated

To find the value of k, which represents the growth rate in the exponential growth function, we need to use the fact that 9 years after 1980, the population increased by 7 million.

In 1980, the population was 29 million, and 9 years later in 1989, it increased to 36 million. Let's substitute these values into the equation A = 29e^(k*t).

A = 29e^(k*9)
36 = 29e^(9k)

To find the value of k, we need to isolate it. Divide both sides of the equation by 29:

36/29 = e^(9k)

Now, take the natural logarithm (ln) of both sides to get rid of the exponential:

ln(36/29) = ln(e^(9k))

Using the property of logarithms that ln(a^b) = b * ln(a), we can simplify further:

ln(36/29) = 9k * ln(e)

The natural logarithm of e (ln(e)) is 1, so we are left with:

ln(36/29) = 9k

Now, divide both sides of the equation by 9:

ln(36/29) / 9 = k

Calculating this expression on a calculator will give us the value of k. Rounded to three decimal places, k ā‰ˆ 0.030.

Therefore, the value of k is approximately 0.030 in the exponential growth function representing the population of the country.