<< Chapter < Page | Chapter >> Page > |
Does a linear, exponential, or logarithmic model best fit the data in [link] ? Find the model.
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | |
3.297 | 5.437 | 8.963 | 14.778 | 24.365 | 40.172 | 66.231 | 109.196 | 180.034 |
Exponential.
While powers and logarithms of any base can be used in modeling, the two most common bases are and In science and mathematics, the base is often preferred. We can use laws of exponents and laws of logarithms to change any base to base
Given a model with the form change it to the form
Change the function so that this same function is written in the form
The formula is derived as follows
Access these online resources for additional instruction and practice with exponential and logarithmic models.
Half-life formula | If the half-life is |
Carbon-14 dating |
is the amount of carbon-14 when the plant or animal died is the amount of carbon-14 remaining today is the age of the fossil in years |
Doubling time formula | If the doubling time is |
Newton’s Law of Cooling | where is the ambient temperature, and is the continuous rate of cooling. |
Notification Switch
Would you like to follow the 'Algebra and trigonometry' conversation and receive update notifications?