A new kind of rocket takes off along an exponential trajectory, with height, in miles, represented by 3x, where x is the time, in seconds. Find the time when the height of the rocket is 8 miles.

What is the exact solution written as a logarithm?

What is an approximate solution rounded to the nearest thousandth?

We have been given that a new kind of rocket takes off along an exponential trajectory, with height, in miles, represented by , where x is the time, in seconds. We are asked to find the time when the height of the rocket id 8 miles.

To find the time, we will equate height function with 8 and solve for x as:

To solve for x, we will take natural log on both sides as:

We can rewrite 8 as .

Using natural log property , we will get:

Therefore, exact solution will be .

Upon rounding to nearest thousandth, we will get:

Therefore, the height of the rocket will be 8 miles after approximately 1.89 seconds.

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step-by-step explanation:

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