Without making any deposit or withdrawal, the initial $10000 will grow at an exponential rate. While the initial amount of $10000 remains unchanged, the amount after x years is [tex]y =10500 \times (1.09)^x[/tex]
Given that the data on the attached table:
An exponential regression equation is represented as: [tex]y = ab^x[/tex]
Where:
[tex]a \to[/tex] initial value
[tex]b \to[/tex] rate
When x = 0, y =10500
[tex]y = ab^x[/tex] becomes
[tex]10500 = ab^0[/tex]
[tex]10500 = a[/tex]
[tex]a=10500[/tex]
When x = 5, y=16000
[tex]y = ab^x[/tex] becomes
[tex]16000 = ab^5[/tex]
Substitute [tex]a=10500[/tex]
[tex]16000 = 10500b^5[/tex]
Divide both sides by 10500
[tex]1.52 = b^5[/tex]
Take 5th root of both sides
[tex]1.09= b[/tex]
[tex]b =1.09[/tex]
So, the exponential equation [tex]y = ab^x[/tex] is:
[tex]y =10500 \times (1.09)^x[/tex]
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