
State the rate of growth given the equation below. 

f(t)=83(1.35) 
t

The equation you've provided, \( f(t) = 83(1.35)^t \), represents an exponential growth model, where:

- The initial value is \( 83 \),
- The growth factor is \( 1.35 \),
- \( t \) is the time.

To determine the rate of growth, we use the growth factor. The rate of growth \( r \) is given by the formula:

\[
r = \text{growth factor} - 1
\]

Substituting the growth factor of \( 1.35 \):

\[
r = 1.35 - 1 = 0.35
\]

Therefore, the rate of growth is 35%.

Would you like a detailed explanation or have any questions?

Here are 5 related questions for further understanding:
1. What is the difference between a growth factor and a growth rate?
2. How would the equation change if the growth rate was 50% instead?
3. How can you determine the initial value from an exponential growth equation?
4. What happens to \( f(t) \) as \( t \) increases in this exponential function?
5. How would you solve for \( t \) if given a specific value of \( f(t) \)?

**Tip**: In exponential growth, the rate is constant, but the value grows faster and faster over time.

State the rate of growth given the equation below. f(t) = 83(1.35)^t

Discover how to calculate the rate of growth from the exponential equation f(t) = 83(1.35)^t. This problem explains key concepts such as growth factor, exponential growth, and how to determine the rate of growth (35%). Ideal for students in Grades 9-12.

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