Suppose that the population of a town is described by P=0.16t^2+7.2t+100, where P is the population in thousands and t is the time in years, (

with t=o representing the year 2000).
A. what will the population be in 2010?
B. what was the population in 1995?
C. when will the population reach 52,000?

For(a) I got P=188,OOO but i do not get the answers for Band C, pLS HELP ME. am sorry for the typing error , the other time.

for B, t = -5

.16*25 - 7.2*5 + 100 = 68 thousand

C
52 = .16 t^2 + 7.2 t +100
solve quadratic. t will be negative of course.

hiloiy

No problem! Let's go step-by-step to solve the problems:

A. To find the population in 2010, we need to substitute t = 10 into the population equation:

P = 0.16(10^2) + 7.2(10) + 100
P = 0.16(100) + 72 + 100
P = 16 + 72 + 100
P = 188 + 100
P = 288

The population in 2010 is 288,000.

B. To find the population in 1995, we need to substitute t = -5 into the population equation:

P = 0.16((-5)^2) + 7.2(-5) + 100
P = 0.16(25) - 36 + 100
P = 4 - 36 + 100
P = -32 + 100
P = 68

The population in 1995 is 68,000.

C. To find when the population reaches 52,000, we need to set the population equation equal to 52:

52 = 0.16t^2 + 7.2t + 100
0.16t^2 + 7.2t + 100 - 52 = 0
0.16t^2 + 7.2t + 48 = 0

At this point, we can solve this quadratic equation using factoring, completing the square, or the quadratic formula. Let's use the quadratic formula:

t = (-b ± √(b^2 - 4ac)) / (2a)

Plugging in the values:
t = (-(7.2) ± √((7.2)^2 - 4(0.16)(48))) / (2(0.16))

Simplifying further:
t = (-7.2 ± √(51.84 - 3.84)) / 0.32
t = (-7.2 ± √48) / 0.32

Now, we can calculate the two possible values for t:

t₁ = (-7.2 + √48) / 0.32 ≈ 13.623
t₂ = (-7.2 - √48) / 0.32 ≈ -5.623

Based on the context, only positive values are relevant for time, so the population will reach 52,000 around 13.623 years after the year 2000.

Hope this helps! Let me know if you have any further questions.

No problem! Let's go through each question step by step.

A. To find the population in 2010, we need to substitute t = 10 into the equation for P. The equation is: P = 0.16t^2 + 7.2t + 100
So, P = 0.16(10)^2 + 7.2(10) + 100
Simplifying this expression, we get P = 0.16(100) + 72 + 100
Now, multiply 0.16 by 100 to get 16, then add 72 and 100 to get the final answer: P = 16 + 72 + 100 = 188.
Therefore, the population in 2010 (in thousands) is 188,000.

B. To find the population in 1995, we need to substitute t = -5 into the equation for P. The equation remains: P = 0.16t^2 + 7.2t + 100
So, P = 0.16(-5)^2 + 7.2(-5) + 100
Simplifying this expression, we get P = 0.16(25) - 36 + 100
Now, multiply 0.16 by 25 to get 4, then subtract 36 and add 100 to get the final answer: P = 4 - 36 + 100 = 68.
Therefore, the population in 1995 (in thousands) is 68,000.

C. To find when the population reaches 52,000, we need to set the equation for P equal to 52 and solve for t. The equation is: P = 0.16t^2 + 7.2t + 100
So, 52 = 0.16t^2 + 7.2t + 100
Rearranging the equation to make it a quadratic equation, we get 0.16t^2 + 7.2t + 100 - 52 = 0
Simplifying this expression, we get 0.16t^2 + 7.2t + 48 = 0

To solve this quadratic equation, you can either factorize it or use the quadratic formula. In this case, factoring might not be easy, so let's use the quadratic formula. The quadratic formula is:

t = (-b ± √(b^2 - 4ac)) / (2a)

In our case, a = 0.16, b = 7.2, and c = 48. Plugging these values into the quadratic formula, we get:

t = (-7.2 ± √(7.2^2 - 4 * 0.16 * 48)) / (2 * 0.16)

Now, simplify the expression inside the square root and proceed with the calculations to find the values of t.