F(x) = 2x ^2 - 6x
1 answer:
The given function is
Here represents the number of rows.
represents the total number of seats in the auditorium.
Now the total seats in the auditorium are 416.
So
Dividing all terms by 2 we get
Subtracting 208 from both sides
Factoring we get
(x-16)(x+13)=0
Using Zero product rule
x - 16= 0 or x+13=0
x= 16 or x = -13
But as x cannot be negative
So x = 16
There are 16 rows in the auditorium if it has a total of 416 seats.
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A typical exponential function is y=a
when x=3.5, y=16.2
when x=6, y=3936.6
plug these values into the exponential function:
16.2=a
3936.6=a
divide the second equation by the first to eliminate a:
243=
log both sides: log243=2.5logb
logb=log243/2.5
use your calculator to find b: b=3.6
plug b=3.6 in the first equation to find a:
16.2=a
a=0.183
please double check my calculation
when x=3.5, y=16.2
when x=6, y=3936.6
plug these values into the exponential function:
16.2=a
3936.6=a
divide the second equation by the first to eliminate a:
243=
log both sides: log243=2.5logb
logb=log243/2.5
use your calculator to find b: b=3.6
plug b=3.6 in the first equation to find a:
16.2=a
a=0.183
please double check my calculation