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Write an exponential equation for each coin that will give the coins value,v,at any time,t use the formula? Coin A worth $25 and increase by 7% each year and coin B worth $40
increase by 5% each year

Respuesta :

deboada35

1) for the coin A  its value to first year , is

a1 = 25+25(7/100)= 25[1+7/100]


the second  year  a2 = a1 + 7/100 a1

a2 = 25+25(7/100) + [25+25(7/100)]7/100

a2= 25+25(7/100) + 25(7/100) + 25(7/100)^2

a2=25[1+7/100]^2

in t years will be at = 25[1+7/100]^t =25[1+0,07]^t

for the coin B IS THE SAME PROCEDURE

bt = 40[1+0,05]^t

Answer: For coin A,

[tex]v=25(1.07)^t[/tex]

For coin B,

[tex]v=40(1.05)^t[/tex]

Step-by-step explanation:

The exponential equation is,

[tex]y=ab^x[/tex]

Where, a is the initial value,

b is the growth or decay factor,

Since, Coin A worth $25 and increase by 7% each year,

So, the coin A's value after t years,

[tex]v=25(1+\frac{7}{100})^t[/tex]

[tex]v=25(1+0.07)^t[/tex]

[tex]\implies v=25(1.07)^t[/tex]

Which is the required equation for coin A.

Now, Coin B worth $40  increase by 5% each year,

So, the coin B's value after t years,

[tex]v=40(1+\frac{5}{100})^t[/tex]

[tex]v=40(1+0.05)^t[/tex]

[tex]\implies v=40(1.05)^t[/tex]

Which is the required equation for coin B.

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