Question

Solve the equation. Round the solution to the nearest tenth . Enter the solution set of the equation . 2P o =P 0 (1.053)^ t

Answer 1

Answer: t= 13.4

Explanation:

The given equation is
`2P_0=P_0(1.053)^t`

To solve this equation for 't', we first divide both sides by
`P_0`, we get

`2=(1.053)^t`

Taking log on both the sides, we get

`\log 2= \log(1.053)^t`

Since
`\log a^b=b\log a`

Then,

`\log 2= t\log1.053\\\\\Rightarrow0.30103=t(0.02243)\\\\\Rightarrow t=(0.30103)/(0.02243)\\\\\Rightarrow t=13.4208649131\approx13.4`

Hence, the value of t is 13.4.