How Long Until?
Part of the Exponentials, Logs & Sequences section of Coddy's Algebra 2 journey. Lesson 6 of 46.
A video has 5 views. The number of views triples every day. On which day does it reach 405? The formula gives the views for a day. How do you find the day from the views?
Write the equation. Then divide both sides by the start, 5: 5 × 3^t = 405 becomes 3^t = 81. Now count the powers of 3: 3, 9, 27, 81. That is 4 of them, so t = 4.
Sometimes the answer is not a whole number. For that you will need a new tool, the logarithm.
Challenge
300 bacteria double every hour. After how many hours t are there 9600? Divide by the start, in your head or on the paper. Then write t = ....
Try it yourself
300 * 2^t = 9600
Solve for t