Question

the number of acres in a landfill is given by the function b(t) = 7300e^(-0.03t), where t is measured in years. how many acres will the landfill have after 3 years? (round to the nearest acre.) 5,934 acres 6,672 acres 7,634 acres 17,578 acres

Explanation:

Step1: Substitute t = 3 into the function

We have the function \( B(t) = 7300e^{-0.03t} \). Substitute \( t = 3 \) into it: \( B(3)=7300e^{-0.03\times3} \)

Step2: Calculate the exponent

First, calculate the exponent: \( -0.03\times3=-0.09 \)

Step3: Calculate the exponential term

Now, calculate \( e^{-0.09} \). We know that \( e^{-0.09}\approx0.9139 \) (using a calculator or known values of the exponential function)

Step4: Multiply by the initial value

Multiply this by 7300: \( 7300\times0.9139\approx7300\times0.914 = 7300 - 7300\times0.086=7300 - 627.8 = 6672.2 \) (rounded to the nearest acre is 6672)

Answer:

B. 6,672 acres