Chapter 9 - Section 9.5 - Exponential and Logarithmic Equations - Exercise Set - Page 730: 143

$t=36$ years

$P_{1}=4000, r_{1}=3\%=0.03, n_{1}=1$ $A_{1}=4000(1+0.03)^t$ $A_{1}=4000(1.03)^t$ and $P_{2}=2000, r_{2}=5\%=0.05, n_{2}=1$ $A_{2}=2000(1+0.05)^t$ $A_{2}=2000(1.05)^t$ $A_{1}=A_{2}$ $4000(1.03)^t=2000(1.05)^t$ $2(1.03)^t=(1.05)^t$ $2=\frac{(1.05)^t}{(1.03)^t}$ $2=(1.02)^t$ $\ln 2=t\ln 1.02$ $t\approx 36$ years