Question

The cost, in dollars, to produce 1 watt of solar energy is a function of the number of years

since 1977.t.
From 1977 to 1987, the cost could be modeled by an exponential function. Here is the
graph of the function.
80
60
dollars per Watt
40
20
4
8
10
6
years since 1977
1. What is the statement f (9) 36 saying about this situation?
2. What is f(4)? What about f (3.5)? What do these values represent in this context?
3. When f(t) = 45, what is t? What does that value of t represent in this context?
4. By what factor did the cost of solar cells change each year? (If you get stuck consider
creating a table.)

Answer 1

In the figure attached, the graph of the function is shown.

1. f(9) ≈ 6 means that at t = 9 (year 1977 + 9 = 1986) the cost to produce 1 watt of solar energy was $6

2. f(4) ≈ 25, which means at year 1981 (=1977 + 4) the cost was $25 per watt

f(3.5) ≈ 28, which means at half of year 1980 (=1977 + 3.5) the cost was $28 per watt

3. When f(t) = 45, t is equal to 2, which means that the year wass 1979 (= 1977 + 2)

4. From the graph we can compute the following table:

x | y

0 | 80

1 | 60

The general exponential decay formula is:

f(x) = a*b^x

where a is the initial value and b si the decay factor. Replacing with data from the table:

f(0) = a*b^0

80 = a

f(1) = a*b^1

60/80 = b

0.75 = b