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Rewrite the function to determine whether it represents exponential growth or exponential decay. Identify the percent rate of change. Round numbers to the nearest hundredth, if necessary. y=(1.06)8t In the form y=a(1+r)t, the function is y≈ . To the nearest percent, the rate of change is a %.

Respuesta :

Answer:

y ≈1*(1+0.59)^t. The rate of change is = 59%

Step-by-step explanation:

We have t mulitplied by 8 in the expression of y. We can write that power with a power of powers, using the property

[tex]a^{bc} = (a^b)^c = (a^c)^b[/tex]

Therefore,

[tex]a^{8t} = (a^8)^t[/tex]  

If we replace a with 1.06, we obtain

[tex] y = 1.06^{8t} = (1.06^8)^t \approx 1.59^t = 1*(1+0.59)^t[/tex]

Thus, y ≈1*(1+0.59)^t. The rate of change is ln(1.59) * 1.59^t. After 1 unit of time t, the rate of change is 0.59*100 = 59%

The rewrite of the function should be [tex]y = 1\times (1+0.59)^t.[/tex]

The rate of change is = 59%

  • The calculation is as follows:

[tex]a^{bc} = (a^b)^c = (a^c)^b[/tex]

So,

[tex]a^{8t} = (a^8)^t\\\\[/tex]

Now

If we replace with 1.06

So,

[tex]y = 1.06^{8t} = (1.06^8)^t = 1\times (1+0.59)^t.[/tex]

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