Question

The population of a large city can be calculated using the function $ P = 156,000(1.07)^{t}$. What can you say about the rate of change from year 1 to year 2 compared to the rate of change from year 9 to year 10?

The rate of change will be the same for all years.
The rate of change will be greater from year 1 to year 2.
The rate of change will be greater from year 9 to year 10.
There is not enough information given.

Answer 1

3. The rate of change will be greater from 9 to year 10

Explanation:

Because this is an exponential function where b 1, the rate of change will be greater from year 9 to year 10.

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Answer 2

The rate of change will be the same for all years. The rate of change is 7%. The . basic formula for this equation is: I(1+R)^T, where I = Initial amount, R = Rate of growth, and T = Time. So the R here is 0.07, or 7%. The growth RATE is constant, the growth AMOUNT will increase each year.