The female silkworm moth secretes pheromone to attract males. When $t$ seconds have passed since the female silkworm moth secreted pheromone, the concentration $y$ of pheromone measured at a distance $x$ from the secretion site satisfies the following equation. $$\log y = A - \frac { 1 } { 2 } \log t - \frac { K x ^ { 2 } } { t } \text { (where } A \text { and } K \text { are positive constants.) }$$ When 1 second has passed since the female silkworm moth secreted pheromone, the pheromone concentration measured at a distance 2 from the secretion site is $a$, and when 4 seconds have passed, the pheromone concentration measured at a distance $d$ from the secretion site is $\frac { a } { 2 }$. What is the value of $d$? [3 points] (1) 7 (2) 6 (3) 5 (4) 4 (5) 3
The female silkworm moth secretes pheromone to attract males.
When $t$ seconds have passed since the female silkworm moth secreted pheromone, the concentration $y$ of pheromone measured at a distance $x$ from the secretion site satisfies the following equation.
$$\log y = A - \frac { 1 } { 2 } \log t - \frac { K x ^ { 2 } } { t } \text { (where } A \text { and } K \text { are positive constants.) }$$
When 1 second has passed since the female silkworm moth secreted pheromone, the pheromone concentration measured at a distance 2 from the secretion site is $a$, and when 4 seconds have passed, the pheromone concentration measured at a distance $d$ from the secretion site is $\frac { a } { 2 }$. What is the value of $d$? [3 points]\\
(1) 7\\
(2) 6\\
(3) 5\\
(4) 4\\
(5) 3