Answer
$$y=e^{5t}+b$$ on condition that $y\gt b$.
Work Step by Step
To solve natural logarithm equations, keep in mind this property:
- If $\ln x = \ln a$ then $x=a$
$$\ln (y-b)=5t$$
- Condition: $y\gt b$
- Recall the property: $\ln e^x=x$
That means $5t=\ln e^{5t}$
Therefore, $$\ln(y-b) = \ln e^{5t}$$
$$y-b=e^{5t}$$
$$y=e^{5t}+b$$
