Question

find the approximate value of h(-2) for the function below. h(x) = 22e^x + 68 a. 2.98 b. 68.14 c. 90.14 d. 70.98

Explanation:

Step1: Substitute \( x = -2 \) into the function \( h(x) = 22e^x + 68 \)

We get \( h(-2)=22e^{-2}+68 \).

Step2: Calculate \( e^{-2} \)

We know that \( e^{-2}=\frac{1}{e^{2}}\approx\frac{1}{7.3891}\approx0.1353 \).

Step3: Calculate \( 22e^{-2} \)

Multiply 22 by the approximate value of \( e^{-2} \): \( 22\times0.1353 = 2.9766\approx2.98 \).

Step4: Calculate \( h(-2) \)

Add 68 to the result of \( 22e^{-2} \): \( h(-2)=2.98 + 68=70.98 \).

Answer:

D. 70.98