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

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

Question
Exponential growth and decay
asked 2020-10-23
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.
\(y=450 \cdot 2^x\)

Answers (2)

2020-10-24
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.
0
2021-06-11

See the solution below:

0

Relevant Questions

asked 2021-05-29
Determine whether each function represents exponential growth or exponential decay. Identify the percent rate of change.
\(\displaystyle{g{{\left({t}\right)}}}={2}{\left({\frac{{{5}}}{{{4}}}}\right)}^{{t}}\)
asked 2021-05-01

Determine whether the function represents exponential growth or exponential decay. Identify the percent rate of change. Then graph the function. \(y=5^x\)

 
asked 2021-05-08
Write an exponential growth or decay function to model each situation. Then find the value of the function after the given amount of time. A new car is worth $25,000, and its value decreases by 15% each year; 6 years.
asked 2021-03-06

Determine whether each equation represents exponential growth or exponential decay. Find the rate of increase or decrease for each model. Graph each equation. \(y=5^x\)

asked 2021-01-31

For the following exercises, determine whether the equation represents exponential growth, exponential decay, or neither. Explain. \(y=11,701(0.97)^t\)

asked 2021-02-04

State whether the equation represents exponential growth, exponential decay, or neither. \(y=0.9^x\)

asked 2021-02-05

Tell whether the function represents exponential growth or decay. \(h(x)=2.5(0.8)^x\)

asked 2020-12-12

Tell whether the function represents exponential growth or exponential decay. Then graph the function. \(f(x)=(1.5)^{x}\)

asked 2021-02-02
Determine whether the function represents exponential growth or exponential decay. Identify the percent rate of change.
\(\displaystyle{y}={3}{\left({1.88}\right)}^{{t}}\)
asked 2020-12-05
Determine whether the function represents exponential growth or exponential decay. Then identify the percent rate of change. y=5(0.6)^t
...