Question

A toy tractor sold for $203 in 1979 and was sold again in 1986 for $427. Assume that the growth in the value V of the collector's item was exponential. A) The value increased by 50%. B) The value doubled. C) The value increased by 110%. D) The value decreased by 50%.

Answer 1

The value of the toy tractor increased by approximately 7.41% from 1979 to 1986, which is closest to option C) The value increased by 110%.

Step-by-step explanation:

To solve this problem, we need to find the growth rate of the value of the toy tractor from 1979 to 1986. We'll use the formula for exponential growth: V = A * (1 + r)^t, where V is the final value, A is the initial value, r is the growth rate, and t is the time period in years.

We can start with the equation V = 203 * (1 + r)^7, where 203 is the value in 1979 and 7 is the number of years between 1979 and 1986.

To determine which option matches the given situation, we can solve for r and compare it to the growth rates given in the options. Let's calculate the growth rate:

1. 427 = 203 * (1 + r)^7
2. (1 + r)^7 = 427/203
3. (1 + r) = (427/203)^(1/7)
4. r ≈ (427/203)^(1/7) - 1
5. r ≈ 0.0741

So, the growth rate is approximately 0.0741 or 7.41%.

Comparing it to the options given, we can see that the value increased by approximately 7.41%, which is closest to option C) The value increased by 110%.

Learn more about Exponential Growth