Okay okay that is correct
Answer:
The linear model means that there is a uniform increase and in this case of US population from 92 million people in 1910 to 250 million people in 1990
.
This means an increase of 250
−
92
=
158 million in 1990
-1910
=
80 years or
158
80
=
1.975 million per year and in x years it will become 92
+
1.975
x million people. This can be graphed using the linear function 1.975
(
x
−
1910
)
+
92
,
graph{1.975(x-1910)+92 [1890, 2000, 85, 260]}
The exponential model means that there is a uniform proportional increase i.e. say p
% every year and in this case of US population from 92 million people in 1910 to 250 million people in 1990
.
This means an increase of 250
−
92
=
158 million in 1990
−
1910
=
80 years or
p
% given by 92
(
1
+
p
)
80
=
250 which gives us (
1
+p
)
80
=
250
92 which simplifies to p
=
(
250
92
)
0.0125
−
1
=
0.0125743 or 1.25743
%
.
This can be graphed as an exponential function 92
×
1.0125743
(
x
−
1910
)
, which gives population in a year y and this appears as
graph{92(1.0125743^(x-1910)) [1900, 2000, 85, 260]}
Step-by-step explanation:
Hope this helps
Answer:
(- 4, - 2 ) and (2, 4 )
Step-by-step explanation:
Given the 2 equations
y = x² + 3x - 6 → (1)
y = x + 2 → (2)
Substitute y = x² + 3x - 6 into (2)
x² + 3x - 6 = x + 2 ( subtract x + 2 from both sides )
x² + 2x - 8 = 0 ← in standard form
(x + 4)(x - 2) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 4 = 0 ⇒ x = - 4
x - 2 = 0 ⇒ x = 2
Substitute these values into (2) for corresponding values of y
x = - 4 → y = - 4 + 2 = - 2 ⇒ (- 4, - 2 )
x = 2 → y = 2 + 2 = 4 ⇒ (2, 4 )
