Question

Determine whether each function represents exponential growth or decay. Write the base in terms of the rate of growth or decay, identify r, and interpret the rate of growth or decay.
\(y=450 \cdot 2^x\)

Answer 1

For an exponential function in the form \(y = a \cdot b^x\)
If b>1 , the function is increasing and is an exponential growth function.
If 0 Because b= 2 > 1, then the function represents an exponential growth. The exponential growth function is given by:
\(A(t)=a(1+r)^t\)
where a is the initial amount, (1+r) is the growth factor, and r is the rate of growth.
Using the value of b,
\(b=1+r \rightarrow 2=1+1\)
Hence, the base in terms of the rate of decay is:
\(y=450(1+1)^x\)
and r is the rate of growth:
\(r=1 \text{ or } 100\%\)
This means that the function increases by 100% as x increases by 1.

Answer 2

See the solution below: