Question

F(t)=30(0.97)∧t whats the rate of change

Answer 1

Hey there, Lets solve this together.


`F(t)=30(0.97)^t`


`A=P(1+r)^t`

The variable (R) will be representing the rate as a decimal.

When you solve for (R) multiply by 100 to get the percentage. A percentage is a rate, number, or amount in each hundred.

"0.97" will be replaced by "(97/100)"

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the given equation


`ft - ((30)) 97/100 ) * t) = 0`

Rewrite the whole as a fraction using 10 as the denominator :


`ft = ft/1 = ft * 10 / 10`

Add the two equivalent fractions which now have a common denominator


`ft * 10 - (291t) / 10 = 10ft - 291t / 10`


`t * (10f - 291) / 10 = 0`


`t*(10f-291) / 10 * 10 = 0 * 10`

The equation now takes the shape :
t • (10f-291) = 0

f = 291/10 = 29.100

t = 0


Positive = Growth

Negative = Decay


`1+r = .97`


`r=-0.03`