Exponential Growth and Decay

$$x>1$$

$$y>1$$

$$x>-2$$

$$y>-2$$

The interest the savings account earned for the first year.

The annual interest rate of the savings account.

The number of years the savings account has earned interest.

The starting balance of the savings account.

$$q\left(x\right)=\left(0.25\right)^x$$

$$q\left(x\right)=256\left(0.25\right)^x$$

$$q\left(x\right)=0.0625\left(4\right)^x$$

$$q\left(x\right)=0.5\left(4\right)^x$$

The initial balance of the account decreases at a rate of $$97.5\%$$ each year.

The balance in the account increases at a rate of $$2.5\%$$ each year.

The initial balance of the account was $1,025.

The balance in the account at the end of one year is $850.

The initial number of bacteria is 12.

The initial number of bacteria decreases at a rate of 88% each day.

The number of bacteria increases at a rate of 12% each day.

The number of bacteria at the end of one day is 245.

$$f\left(x\right)=1,024\left(1.50\right)^x$$

$$f\left(x\right)=1,024\left(0.50\right)^x$$

$$f\left(x\right)=1,024\left(1.05\right)^x$$

$$f\left(x\right)=1,024\left(0.05\right)^x$$

$$c\left(x\right)=495,000\left(1.0325\right)^x$$

$$c\left(x\right)=495,000\left(0.9675\right)^x$$

$$c\left(x\right)=495,000x^{1.0325}$$

$$c\left(x\right)=495,000x^{0.9675}$$

$$n=4\left(\frac{1}{2}\right)^h$$

$$n=4\left(2\right)^h$$

$$n=4+\left(2\right)^h$$

$$n=4+\left(\frac{1}{2}\right)^h$$