Even when the surroundings suddenly become dark, the human eye perceives the change gradually. After the light intensity suddenly changes from 1000 to 10 and $t$ seconds have elapsed, the light intensity $I ( t )$ perceived by a person is $$I ( t ) = 10 + 990 \times a ^ { - 5 t } ( \text { where } a \text { is a constant with } a > 1 )$$ After the light intensity suddenly changes from 1000 to 10, let $s$ seconds elapse until the person perceives the light intensity as 21. What is the value of $s$? (Note: The unit of light intensity is Td (troland).) [3 points] (1) $\frac { 1 + 2 \log 3 } { 5 \log a }$ (2) $\frac { 1 + 3 \log 3 } { 5 \log a }$ (3) $\frac { 2 + \log 3 } { 5 \log a }$ (4) $\frac { 2 + 2 \log 3 } { 5 \log a }$ (5) $\frac { 2 + 3 \log 3 } { 5 \log a }$
Even when the surroundings suddenly become dark, the human eye perceives the change gradually. After the light intensity suddenly changes from 1000 to 10 and $t$ seconds have elapsed, the light intensity $I ( t )$ perceived by a person is
$$I ( t ) = 10 + 990 \times a ^ { - 5 t } ( \text { where } a \text { is a constant with } a > 1 )$$
After the light intensity suddenly changes from 1000 to 10, let $s$ seconds elapse until the person perceives the light intensity as 21. What is the value of $s$? (Note: The unit of light intensity is Td (troland).) [3 points]\\
(1) $\frac { 1 + 2 \log 3 } { 5 \log a }$\\
(2) $\frac { 1 + 3 \log 3 } { 5 \log a }$\\
(3) $\frac { 2 + \log 3 } { 5 \log a }$\\
(4) $\frac { 2 + 2 \log 3 } { 5 \log a }$\\
(5) $\frac { 2 + 3 \log 3 } { 5 \log a }$