Question

Solve the following formula for t.
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:
\[
t = \frac{A - U}{Ur}
\]