Question 121·Easy·Nonlinear Functions
For the function defined above, what is the value of ?
For function-evaluation questions, go step by step: carefully substitute the given input into the variable, respect the order of operations (exponents first, then multiplication), and do the arithmetic cleanly. With decimals, remember that squaring a number less than 1 makes it smaller (e.g., should be less than 0.4), which helps you quickly eliminate answers that are too large or based on incorrect exponent handling.
Hints
Use the definition of the function
You are given . To find , replace with 2 everywhere it appears in the formula.
Handle the exponent first
After substituting , focus on evaluating . Remember that an exponent of 2 means multiplying the base by itself.
Finish with multiplication
Once you know the value of , multiply that result by 5 to get , then match your result to the closest answer choice.
Desmos Guide
Evaluate the function at t = 2
In Desmos, type 5*(0.4)^2 into an expression line. The numeric result that appears is the value of ; compare that value with the answer choices and select the matching one.
Step-by-step Explanation
Substitute the given input into the function
The function is and we are asked for .
Substitute into the function:
Evaluate the exponent
Now compute .
Remember that squaring means multiplying the number by itself:
So now we have:
Multiply to get the final value
Now multiply 5 by :
So , which matches answer choice B.