Answer:
- y = 22·e^(0.3001t), growing
- annual rate: 35%
- continuous rate: 30.01%
Step-by-step explanation:
When an exponential function is in the form ...
y = ab^t
the factor 'b' is called the growth factor. When t is in years, it is related to the annual growth rate (r) by ...
b = 1 +r
In the alternate form, this can be written ...
y = a·e^(kt)
Comparing the forms, we see that ...
b = e^k ⇒ k = ln(b)
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<h3>(a)</h3>
y = 22·1.35^t
k = ln(1.35) ≈ 0.3001
y = 22·e^(0.3001t)
The growth factor is greater than 1, so the function is growing.
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<h3>(b)</h3>
The annual growth rate is ...
r = 1.35 -1 = 0.35 = 35.00%
__
<h3>(c)</h3>
The continuous growth rate is ...
k = 0.3001 = 30.01%
