37: 37
144: 2 x 2 x 2 x 2 x 3 x 3
147: 3 x 7 x 7
205: 5 x 41
Dp/dt = .0375 people/year
<span>ln p = .0375 t + c </span>
<span>p = c e^(.0375 t) </span>
<span>when t = 0, p = 500,000 </span>
<span>so </span>
<span>p = 500,000 e^(.0375 t) </span>
<span>so </span>
<span>2 = 1,000,000/500,000 = e^(.0375 t) </span>
<span>ln 2 = .0375 t </span>
<span>t = 18.5 years</span>
Answer: Joe hit the target 4 times.
Explanation: We can write this scenario as a system of equations.
Let’s express the number of times he hits the target with x.
Let’s express the number of times he misses the target with y.
“He earned 20 points each time he hit the target but lost 50 points when he miss. Joe ended the night with negative 470 points...”
20x - 50y = -470
“...after 15 shots.”
x + y = 15
Let’s write the whole system of equations.
20x - 50y = -470
x + y = 15
Let’s solve the second equation for y.
x + y = 15
Subtract x from both sides.
y = 15 - x
Let’s substitute y in the first equation with 15 - x.
20x - 50(15 - x) = -470
Distribute -50 among 15 and -x in the term -50(15 - x).
20x - 750 + 50x = -470
Combine like terms on the left side.
70x - 750 = -470
Add 750 on both sides.
70x = 280
Divide both sides by 70.
x = 4
Since we know that x = 4, we know that Joe hit the target 4 times.
45 divided by 5 is 9, s=9.
