Complete the explicit formula for the sequence. 42, 47, 52, 57, 62, ...
1 answer:
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Answer:
y = 9x - 11
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (- 3, - 38) and (x₂, y₂ ) = (8, 61)
m = =
= 9, thus
y = 9x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation
Using (8, 61), then
61 = 72 + c ⇒ c = 61 - 72 = - 11
y = 9x - 11 ← equation of lie
Given:
f(x) is an exponential function.
To find:
The value of f(6.5).
Solution:
Let the exponential function is
...(i)
Where, a is the initial value and b is the growth factor.
We have, . So, put x=-3.5 and f(x)=25 in (i).
...(ii)
We have, . So, put x=6 and f(x)=33 in (i).
...(iii)
On dividing (iii) by (ii), we get
Putting b=1.03 in (iii), we get
Putting a=27.63 and b=1.03 in (i), we get
Therefore, the required exponential function is .