Question

15(1+0.6/4)^4t = 30e^-0.25t, solve for t

Answer 1

Answer: x =
`-(ln(0.5))/(4ln(1.15) + 0.25)`

≈ 0.856

Explanation:

15(1 +
`(0.6)/(4)`)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
`(1)/(2)` + 4x ln(1.15) = -0.25x

4x ln(1.15) + 0.25x = -ln
`(1)/(2)`

x(4 ln(1.15) + 0.25) = -ln 0.5

x =
`-(ln(0.5))/(4ln(1.15) + 0.25)`

≈ 0.856