the number of cats that are homeless can be modeled by the equation N= 2.1t squared - 82t + 95 where N is the number of cats that are homeless and t=0 set as the current year.Use the quadratic model to find the number of years from now until the number of homeless cats is equal to 15.need larger number of the two answers to the nearest hundredth.

2.1t^2 - 82t + 95 = 15

2.1t^2 - 82t + 80 = 0

solve using the quadratic equation formula, I got
t = 1.00 or t =38.05

N=2.1t^2- 82t+95 Since N = 15,

15=2.1t^2- 82t+95 Now get this quadratic into standard form by subtracting 15 from both sides

15-15= 2.1t^2- 82t+95-15
0=2.1t^2- 82t+80 I am not sure what methods you have studied to solve this yet, but I would use the quadratic equation. Where a = 2.1, b = 82 and c = 80
t= (-b�}�ã(b^2-4ac))/2a
t= (-82�}6052)/(2(2.1))
t = -1.00 or -38.04
Largest would be -1.00

To find the number of years from now until the number of homeless cats is equal to 15, we need to solve the equation N = 15 for t, which represents the number of years from the current year.

Given the equation N = 2.1t^2 - 82t + 95, we substitute N with 15:

15 = 2.1t^2 - 82t + 95

Rearranging the equation and collecting like terms:

2.1t^2 - 82t + 95 - 15 = 0

2.1t^2 - 82t + 80 = 0

Now we have a quadratic equation in the form of at^2 + bt + c = 0, where a = 2.1, b = -82, and c = 80.

To solve this quadratic equation, we can use the quadratic formula:

t = (-b ± √(b^2 - 4ac)) / (2a)

Plugging in the values:

t = (-(-82) ± √((-82)^2 - 4(2.1)(80))) / (2(2.1))

Simplifying:

t = (82 ± √(6724 - 672)) / 4.2

t = (82 ± √6052) / 4.2

We have two potential solutions: t1 and t2.

t1 = (82 + √6052) / 4.2

t2 = (82 - √6052) / 4.2

Calculating the values:

t1 ≈ 31.69 (rounded to two decimal places)

t2 ≈ -1.15 (rounded to two decimal places)

Since the number of years cannot be negative in this context, we discard t2 as a valid solution.

Therefore, the larger number of the two answers is approximately 31.69 years from now.