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).
I just need help getting started with this one.
To find the exponential curve through the points (7, 10) and (9, 250), we need to determine the values of A and b in the equation y = A ¢ bx.
Step 1: Substitute the first point (7, 10) into the equation y = A ¢ bx.
10 = A ¢ b^7
Step 2: Substitute the second point (9, 250) into the equation y = A ¢ bx.
250 = A ¢ b^9
Now we have a system of two equations with two variables (A and b). We can solve this system to find the values of A and b.
Step 3: Divide the two equations to eliminate A:
(10 / 250) = (A ¢ b^7) / (A ¢ b^9)
1/25 = 1/b^2
b^2 = 25
b = √25
b = 5
Step 4: Substitute the value of b back into one of the original equations (step 1 or 2) to solve for A.
10 = A ¢ 5^7
10 = A ¢ 78125
A = 10 / 78125
A ≈ 0.000128
Therefore, the exponential curve through the points (7, 10) and (9, 250) is given by the equation:
y ≈ 0.000128 ¢ 5^x