The exponential function is :
y=ab^x
We have two points:
(1, 7.5)
(3, 16.875)
First point:
(1 , 7.5)
x=1
y=7.5
y=ab^x
7.5=ab¹
Second point:
(3 , 16.875)
x=3
y=16.875
y=ab^x
16.875=ab³
Then, always is true that.
7.5 / 16.875 = (ab) / (ab³)
7.5(ab³)=16.875(ab)
7.5ab³ / a
b²=16.875
7.5b²=16.875
b=⁺₋√(16.875 / 7.5)
b=⁺₋1.5
if b=-1.5 ⇒ 7.5=a(-1.5) ⇒a=-5
y=-5*(-1.5)^x
y=5(1.5^x)
if b=1.5 ⇒ 7.5=a(1.5) ⇒ a=5
y=5*(1.5^x)
Answer; y=5*1.5^x
Answer:
f(-2) = 13
g(4) = -9
Explanation:
Whenever a question is asking you to find something like, in this example, f(-2) or g(4), you have to substitute whatever number is in the parentheses for every x in the function with that letter.
Let's try to find f(-2). We have to substitute -2 for every x in the function f and simplify:
![f(-2) = -2 (-2)^{3} -3\\f(-2) = -2(-8)-3\\f(-2) = 16 - 3 \\f(-2) = 13](https://tex.z-dn.net/?f=f%28-2%29%20%3D%20-2%20%28-2%29%5E%7B3%7D%20-3%5C%5Cf%28-2%29%20%20%3D%20-2%28-8%29-3%5C%5Cf%28-2%29%20%3D%2016%20-%203%20%5C%5Cf%28-2%29%20%20%3D%2013)
Therefore,
.
Next, let's try to find g(4). We have to substitute 4 for every x in the function g and simplify:
![g (4) = -2(4) - 1\\g(4) = -8-1\\g(4) = -9](https://tex.z-dn.net/?f=g%20%284%29%20%3D%20-2%284%29%20-%201%5C%5Cg%284%29%20%3D%20-8-1%5C%5Cg%284%29%20%3D%20-9)
Therefore, ![g (4) = -9.](https://tex.z-dn.net/?f=g%20%284%29%20%3D%20-9.)
Answer:
The inverse operation is division
Answer:
12,600 after 3 years with no withdrawals.