Question

identify the initial amount,a,and the growth factor,b,in each exponential function.Break b into (1+r)where r is the rate of growth. Give r as a percentage. y=1.05(1.46)^x

Answer 1

Given function :
`y=1.05(1.46)^x`

We need to identify a " initial amount", b "growth factor", r " rate of growth".

We know, exponential growth formula

`y=a(b)^x`, where a is initial amount, b is growth factor. On comparing with given function let us find values of a and b.

`y=1.05(1.46)^x` ⇔
`y=a(b)^x`.

We can see a= 1.05 and b = 1.46.

Now, b=1+r.

Therefore, 1+r =1.46.

Subtracting 1 from both sides, we get

1+r-1 =1.46-1

r = 0.46.

On converting 0.46 into percentage, we get

0.46 × 100 = 46.

Therefore, intial amount a = a= 1.05 , growth factor b = 1.46, and the rate of growth r= 46%.