You are starting a babysitting business to earn enough money to buy a new iPhone 7 Plus, which costs $769. You already have $240
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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.