csat-suneung· South-Korea· csat__math-science3 marks
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 $$I ( t ) = 10 + 990 \times a ^ { - 5 t } \text{ (where } a \text{ is a constant with } a > 1 \text{)}$$ 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 $s$? (Here, 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
$$I ( t ) = 10 + 990 \times a ^ { - 5 t } \text{ (where } a \text{ is a constant with } a > 1 \text{)}$$
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 $s$? (Here, 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) $\frac { 2 + 3 \log 3 } { 5 \log a }$