Solve the following formula for t.

Question

Upper A equals Upper U left parenthesis 1 plus rt right parenthesis
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Part 1
The solution is tequals
  
enter your response here. ​(Simplify your​ answer.)

Answer 1

To solve the equation $A=U(1+rt)$ for $t$, follow these steps:

1. Isolate the term involving $t$: $$A=U(1+rt)$$ Dividing both sides by $U$: $$\frac{A}{U}=1+rt$$

2. Subtract 1 from both sides: $$\frac{A}{U}-1=rt$$

3. Reorganize the left side: $$\frac{A-U}{U}=rt$$

4. Finally, isolate $t$: $$t=\frac{\frac{A-U}{U}}{r}$$ Simplifying it further: $$t=\frac{A-U}{Ur}$$

Thus, the solution for $t$ is: $$t=\frac{A-U}{Ur}$$