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.
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1b. For t=4, we have ...
E = 5·1.59^4 ≈ 31.96 ≈ 32
About 32 GWh was generated in 1984.
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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.
