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3 years ago

6

In 1980, wind turbines in Europe generated about 5 gigawatt-hours of energy. Over the next 15 years, the amount of energy increa

se by about 59% per year.
NOT A MULTIPLE CHOICE

1a. Write a model giving the amount E of energy t years after 1980.

1b. Use your model determine how much wind energy was generated in 1984.

1c. Determine the year when 80 gigawatt-hours of energy were generated.

1 answer:

sammy [17]3 years ago

4 0

9514 1404 393

Answer:

1a. E = 5×1.59^t

1b. 32 GWh

1c. 1986

Step-by-step explanation:

1a. An exponential model looks like

f(t) = a·b^t

where 'a' is the value when t=0, and 'b' is the growth factor in the time period associated with t.

Here, 'a' is 5 (GWh), and 'b' is 1+59% = 1.59. Then the desired model is ...

E = 5·1.59^t . . . . . where t is years after 1980, and E is in GWh.

__

1b. For t=4, we have ...

E = 5·1.59^4 ≈ 31.96 ≈ 32

About 32 GWh was generated in 1984.

__

1c. The value of t for a given value of E is ...

E/5 = 1.59^t . . . . divide by 5

log(E/5) = t·log(1.59) . . . . take logarithms

t = log(E/5)/log(1.59) . . . . divide by the coefficient of t

For E = 80, the years after 1980 are ...

t = log(80/5)/log(1.59) ≈ 5.98

About 80 GWh were generated in 1986.

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