Find the exponential curve through (7, 10) and (9, 250). Recall that an exponential curve is one given by the equation y = A * bx (i.e. is the set of all points (x,A * bx).
y = A * bx is not an exponential equation.
Did you mean
y = A * b^x ?
confirm before I start working on it.
Yes that is how it is. sorry i am not good at typing them out
sub in each point
equation #1:
10 = A(b^7)
equation #2:
250 = A(b^9)
divide equation 2 by equation 1, the A's will cancel, to get
b^2 = 25
b = 5 , (or -5, but in exponentioal equations the base is considered positive)
back in #1
10 = A(5^7)
A = 10/78125
so y = (10/78125)(5^x)
check for (9,250)
LS = 250
RS = (10/78125)(5^9) = 250 , YEAHHH!
To find the exponential curve that passes through the given points, we can use the equation y = A * bx. Let's label the first point as (x1, y1) = (7, 10) and the second point as (x2, y2) = (9, 250).
Using the equation for the first point (7, 10), we have:
10 = A * b^7
Using the equation for the second point (9, 250), we have:
250 = A * b^9
Now, we can divide the second equation by the first equation to eliminate A:
(250/10) = (A * b^9) / (A * b^7)
Simplifying,
25 = b^2
Taking the square root,
5 = b
Now, we can substitute the value of b back into the first equation to find A:
10 = A * 5^7
Simplifying,
10 = 78125A
Dividing both sides by 78125,
A = 10 / 78125
Therefore, the equation for the exponential curve that passes through the points (7, 10) and (9, 250) is:
y = (10 / 78125) * 5^x