GED Mathematical Reasoning TestAlgebraic Problem Solving with Expressions and EquationsMedium
A botanist is studying the growth of a rare plant species. The height of the plant, H, in centimeters, is modeled by the function H(t) = 3(1.15)^t, where 't' is the number of weeks after planting. What is the approximate height of the plant after 5 weeks?
- A8.32 cm
- B7.54 cm
- C6.03 cm
- D3.45 cm
Show answer & explanationAnswer & explanation
Correct answer: C. 6.03 cm
To find the height after 5 weeks, substitute t=5 into the function: H(5) = 3(1.15)^5. First, calculate (1.15)^5 ≈ 2.011357. Then, multiply by 3: H(5) ≈ 3 * 2.011357 ≈ 6.034071. Rounded to two decimal places, the height is approximately 6.03 cm.
Why the other options are wrong
- A. This could be a result of calculation errors, possibly using t=6 instead of t=5 or other miscalculations.
- B. This could be a result of calculation errors in the exponentiation or multiplication.
- D. This might come from 3 * 1.15 = 3.45, which only accounts for one week's growth or a misinterpretation of the exponent.
Evaluating Exponential Functions
Evaluating an exponential function involves substituting a given value for the independent variable (usually time) into the function and calculating the resulting dependent variable.
- Follow the order of operations (PEMDAS/BODMAS).
- Calculate the exponentiation first, then multiplication.
- Use a calculator for accurate results with decimals and exponents.
Memory trick: Plug in 't', power up, then multiply.