Question

Tai notices that although his little brother is not growing by the same amount each month, there is a pattern in how quickly he is growing. Tai determines that each month his brother grows more than he grew the previous month. What type of function could represent Tai's brother's growth? Select one: A. A linear function, because linear functions increase at a constant rate B. A linear function, because linear functions increase at a nonconstant rate C. An exponential function, because exponential functions increase at a constant rate D. An exponential function, because exponential functions increase at a nonconstant rate

Answer 1

D. An exponential function, because exponential functions increase at a nonconstant rate

Explanation:

Each month Tai's brother grows more than he grew the previous month.

We can't model his growth by a linear function, because linear functions increase at a constant rate.

The model must be an exponential function.

For example, if the boy's height at Month 0 were 100 units, a model like h = 100(1.1)ⁿ would give the following results.

`\begin{array}{ccc}\textbf{Month} & \textbf{Height} & \textbf{Diff.}\\0 & 100 & \\1 & 110 & 10\\2 & 121 & 11\\3 & 133 & 12\\4 & 146 & 13\\\end{array}`

An
`\boxed{\textbf{ exponential function }}` is consistent with a monthly change in height that increases each month.