Final answer:
The student's question requires constructing an exponential function for modelling data over time and understanding growth rate scenarios. It involves exponential functions, predictions, and solving for variables using quadratic equations.
Step-by-step explanation:
The question asks for help in determining an exponential function of the form f(t)=y₀b based on given data with a specific application to growth over time. This function can be modeled for different scenarios, such as predicting sales growth or analyzing physical phenomena with exponential characteristics.
The values provided in various parts of the question indicate typical parameters such as base growth rates or initial values that are needed to construct an accurate model.
For instance, when predicting growth over a 10-year period, if we use equation outputs like M = 1.63, this suggests a 63% increase in size. Alternatively, if using b = 1.05 and n = 10, we would also reach an equivalent result reflecting the exponential growth.
When dealing with different bases such as 10, factors such as natural logarithms come into play, particularly when a 2.3% growth rate is present.
Moreover, some questions involve solving quadratic equations, where numbers provided represent coefficients in equations, such as the quadratic equation at² + bt + c = 0. The solution to these equations employs the quadratic formula, which is a fundamental tool in algebra.