Question

My problem is I don't know how to write an equation into exponential growth, or exponential decay.

To further explain, here is the math problem:

Rewrite y = 2(1.06)^9t in the form y = a(1+r)^t or y = a(1-r)^t to determine whether it represents exponential growth or exponential decay. Round a and r to the nearest hundredth if necessary.

I have a 2nd math problem that's just like this, but with a different equation. Can anyone help me and also teach me the way to find the answer? My notes does not cover this.

Answer 1

Answer: y = 2( 1 + 0.69 )^t

This is exponential growth

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Step-by-step explanation:

The exponential rule we need is: a^(b*c) = (a^b)^c

Apply that rule and do a bit of rearranging:

y = 2(1.06)^(9t)

y = 2( (1.06)^9 )^t

y = 2( 1.68948 )^t

y = 2( 1 + 0.68948 )^t

y = 2( 1 + 0.69 )^t

The last equation fits the format of y = a(1+r)^t which tells us that...

• a = 2
• r = 0.69 approximately

Since r is positive, we have exponential growth. If r was negative, then we'd have exponential decay.