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

Step-by-step 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,

$\log 2= t\log1.053\\\\\Rightarrow0.30103=t(0.02243)\\\\\Rightarrow t=\dfrac{0.30103}{0.02243}\\\\\Rightarrow t=13.4208649131\approx13.4$

Hence, the value of t is 13.4.