Problem 86 - College Algebra

Question

The function \(W(t)=2600\left(1-0.51 e^{-0.075 t}\right)^{3}\) models the weight, \(W(t),\) in kilograms, of a female African elephant at age \(t\) years. (1 kilogram \(\approx 2.2\) pounds) Use a graphing utility to graph the function. Then \([\text { TRACE }]\) along the curve to estimate the age of an adult female elephant weighing 1800 kilograms.

Step-by-Step Solution

Answer

The estimation of the age of a female African elephant weighing 1800 kilograms can only be determined precisely using an actual graphing utility. Following the steps outlined, anyone can easily find the estimate.

Step 1: Graph the function

Begin by plotting the function \(W(t)=2600\left(1-0.51 e^{-0.075 t}\right)^{3}\) using any available graphing utility. This should provide a visual representation of how the elephant's weight varies with age.

Step 2: TRACE along the curve

Using the TRACE feature on the graphing utility, move along the curve until reaching the desired weight. TRACE allows real-time visualization of the coordinates (t,W(t)) on the graph.

Step 3: Estimate the age

Once the weight of 1800 kg is located on the graph, check the 't' value (as Y-value corresponds to W(t), the weight, and X-value corresponds to 't', the age). This 't' value correlates to the estimated age of the elephant when its weight is 1800 kg.