Скачать или смотреть L.C. Maths O.L. 2024 Q7 (b): Exponential Function & Natural Log (Finding Time)

🔥 Leaving Cert Maths O.L.: Exponential Functions - Conquer the Natural Log (ln)! 🔥

This video provides the full solution for *Question 7 (b)* from the *LCOL 2024 Paper 1* (50 marks!). This question introduces the exponential function model for a different bacteria population.

We guide you through the three tricky parts:
*Part (i):* Using the Natural Log Scale—we show you how to correctly plot the points on the provided graph, which is essential for understanding exponential growth.
*Part (ii):* Finding the population at a specific time (t=6)—a simple calculator substitution.
*Part (iii) (CRUCIAL!):* Solving the equation to find the exact time ($t$) when the population reaches a specific number. This requires using the *Natural Logarithm ($\ln$)* to "undo" the $e$ power.

Don't panic when you see $e$! We make the use of the Natural Log function simple and clear.

⏱️ Timestamps (Use double line breaks when copying to YouTube):

0:00 - Introduction to LCOL 2024 Q7 (Exponential Function)
1:33 - *Part (i):* Plotting the Points on the Natural Log Scale
3:02 - *Part (ii):* Finding the Population when time (t) = 6
4:05 - *Part (iii):* Setting up the Equation for Solving for Time ($t$)
5:01 - *Part (iii):* Using the Natural Log ($\ln$) to solve for $t$
6:30 - The Final Answer Correct to Two Decimal Places