Answer: x = [tex]-\frac{ln(0.5)}{4ln(1.15) + 0.25}[/tex]
≈ 0.856
Step-by-step explanation:
15(1 + [tex]\frac{0.6}{4}[/tex])⁴ˣ = 30e⁻°²⁵ˣ
15(1.15)⁴ˣ = 30e⁻°²⁵ˣ
÷30 ÷30
0.5(1.15)⁴ˣ = e⁻°²⁵ˣ
ln[0.5(1.15)⁴ˣ] = ln[e⁻°²⁵ˣ]
ln 0.5 + ln(1.15)⁴ˣ = -0.25x
ln[tex]\frac{1}{2}[/tex] + 4x ln(1.15) = -0.25x
4x ln(1.15) + 0.25x = -ln[tex]\frac{1}{2}[/tex]
x(4 ln(1.15) + 0.25) = -ln 0.5
x = [tex]-\frac{ln(0.5)}{4ln(1.15) + 0.25}[/tex]
≈ 0.856
