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2 years ago

Write the exponential function y = 22(1.35)' in the form y = aekt.

Mathematics

1 answer:

vesna_86 [32]2 years ago

4 0

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)

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.

The annual growth rate is ...

r = 1.35 -1 = 0.35 = 35.00%

The continuous growth rate is ...

k = 0.3001 = 30.01%

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Step-by-step explanation:

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2 years ago

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Taxi B
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3miles £3.50+£5.25=£8.75
Taxi B
3miles £1.25+£6.00=£7.25

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4miles £3.50+£7.00=£10.50
Taxi B
4miles £1.25+£8.00=£9.25

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5miles £3.50+£8.75=£12.25
Taxi B
5miles £1.25+£10.00=£11.25

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6miles £3.50+£10.50=£14.00
Taxi B
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Taxi B
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