Problem preview

F-BF.1.a Warmup M2-014-A14-V03

Build quadratic and exponential functions from context using explicit formulas, recursive processes, or calculation steps.

Build an explicit model from context and solve for the input that gives a target output

Problem

An account balance after $t~\text{whole}~\text{hours}$ is $A(t)=100\cdot~2^t~\text{dollars}$. Find when the balance reaches $\$800$ by isolating $2^t$ and expressing $8$ as a power of $2$. Check the result against the nonnegative whole-hour domain and verify it in $A(t)$.

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The solutions are t = −3 and 3 hours. Only t = 3 satisfies 2t = 8 and the nonnegative whole-hour context.

Set A(t) = 800, but no account model or algebraic reduction is supplied, so no time can be determined.

A(t) = 100 · 2t. Setting A(t) = 800 gives 2t = 8 = 2³, so t = 3; it is a valid whole hour, and 100 · 8 = 800.

The target $800 is treated as input t = 800. The target amount is an output, and no valid-time check is supplied.

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Curriculum context

Course: Math II
Standard: F-BF.1.a
Category: Functions
Domain: Building Functions
Objective: Build quadratic and exponential functions from context using explicit formulas, recursive processes, or calculation steps.
Problem type: Build an explicit model from context and solve for the input that gives a target output