Logarithmic Function

A small business owner uses a financial tool to compare two different savings accounts that grow at the same monthly rate. The tool generates the equation ${}1.01^t = 1.01^{24}$ to determine when the account balances will be identical. Which property of exponential functions allows the owner to conclude that $t = 24$?

An operations manager at a logistics company uses an exponential function to model package sorting times. When analyzing the model's equations to determine when two processing times with the same base rate will be equal ($a^x = a^y$), the manager applies the rule that the inputs must also be equal ($x = y$). Graphically, this one-to-one property is demonstrated because the exponential model passes the ________.

A data analyst is validating an exponential growth model used to forecast company revenue. Match each aspect of the exponential function's "one-to-one" nature with its corresponding mathematical or graphical description.

An environmental scientist is using an exponential model to track the decay of a substance over time. If the model leads to the equation $b^x = b^y$ (where the base $b > 0$ and $b eq 1$), is it true that the one-to-one property of exponential functions allows the scientist to conclude that $x = y$?

Applying the One-to-One Property in Technical Modeling