Question

The currrent, I0 (measured in amperes), decreases to I amperes after t seconds according to the formula I = I0e−0.51t. When 8 amperes decreases to 3.2 amperes, the equation is 3.2 = 8e−0.51t. Rounded to the nearest tenth of a second, how long, t, does it take for the current to decrease from 8 amps to 3.2 amps?

Answer 1

the time it takes for the current to decrease from 8 amperes to 3.2 amperes is 1.7966, we use the given decay formula and solve for t by rearranging the equation and applying logarithmic operations.

Step-by-step explanation:

The student asks how long it takes for the current to decrease from 8 amperes to 3.2 amperes using the exponential decay formula I = I0e-0.51t.

To solve for t, we'll rearrange the equation to solve for t after substituting the given values:

3.2 = 8e-0.51t

0.4 = e-0.51t

ln(0.4) = -0.51t

t = -ln(0.4) / 0.51

= 1.7966

the time required for the current to decrease to the given value.