Given:
An exponential function goes through points (0,12) and (3,6144).
To find:
The exponential function.
Solution:
The general exponential function is:
...(i)
The function goes through point (0,12). Substituting , we get
The function goes through point (3,6144). Substituting in the general exponential function, we get
Putting in (i), we get
Therefore, the required exponential function is .
Answer:
see explanation
Step-by-step explanation:
(1)
Given
g(r) = (r + 14)² - 49
To obtain the zeros, let g(r) = 0 , that is
(r + 14)² - 49 = 0 ( add 49 to both sides )
(r + 14)² = 49 ( take the square root of both sides )
r + 14 = ± = ± 7 ( subtract 14 from both sides )
r = - 14 ± 7, then
r = - 14 - 7 = - 21 ← smaller r
r = - 14 + 7 = - 7 ← larger r
(2)
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
g(r) = (r + 14)² - 49 ← is in vertex form
with vertex = (- 14, - 49 )