options: Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.

Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).

Distinguish between situations that can be modeled with linear functions and with exponential functions.

For exponential models, express as a logarithm the solution to ab^(ct) = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology.
problem_activity: 1. A youth group has a yard sale to raise money for a charity. The group earns $800 but decides to put its money in the bank for a while. The group considers two different banks:
Cool Bank pays simple interest at a rate of 4%, and the youth group plans to leave the money in the bank for 3 years.
Hot Bank pays an interest rate of 3% compounded annually, and the youth group plans to leave the money in the bank for 5 years.
Write a function to represent the amount of money earned at each bank. Then determine how much money the youth group would earn in each situation.
2. If the youth group needs the money quickly, which is the better choice? Explain your reasoning.


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