A filter circuit is activated when the current reaches 5 amperes. If a charge is fed to the circuit starting at 1 ampere and is steadily increased by 50% of the current value every 10 seconds, how long will it be until the filter activates?

3.69 seconds
10.50 seconds
39.69 seconds
40.00 seconds

Question

A filter circuit is activated when the current reaches 5 amperes. If a charge is fed to the circuit starting at 1 ampere and is steadily increased by 50% of the current value every 10 seconds, how long will it be until the filter activates?

3.69 seconds
10.50 seconds
39.69 seconds
40.00 seconds

yttrium · Answer

does it something to do with integration?

ganeshie8 · Answer

final value = 5 amperes
initial value = 1 ampere
rate =  1 + 0.5 = 1.5 every 10 seconds

set up a growth equaiton

ganeshie8 · Answer

$\large   5 =   (1.5)^{\frac{t}{10}}$

ganeshie8 · Answer

solve $t$