Question

A dolldoll sold for ​$277 in 1980 and was sold again in 1986 for $434. Assume that the growth in the value V of the​ collector's item was exponential.
​a) Find the value k of the exponential growth rate. V subscript o=277.

Answer 1

hi okay, they want u to assume there was some exponential growth rate per year*

Answer 2

i am not sure if you've been introduced to writing exponential formulas with the base e
in the form
Y=Ae^(kt)

Answer 3

if you are not, you can still use the same logic as before, suppose there is some growth rate per year

Answer 4

if u have a growth rate g for 6 years we have
277(1+g)^6=434
we can solve for g

Answer 5

or with this equation
Y=Ae^(kt)
434=277e^(k*6)
solve for k

Answer 6

this k is going to be different from the g btw, because its a continuous growth rate vs incremental growth rate

Answer 7

We do write with base e! :)

Answer 8

okay solve for k there

Answer 9

u can use this
Y=xe^(kt)
then
(Y/x) = e^(kt)
ln(Y/x)=kt
k=(ln(Y/x))/t

Answer 10

Using "x" as a constant here is not wise.

I propose you use the exponential growth formula\[A=A _{0}Ce ^{kt}\]

Answer 11

where A would represent the value of the doll in 1986, A_0 is the value of the doll in 1980, and k is the exponential growth constant. (Cross out the "C" in the above equation; do not use it.)

Answer 12

t represents the number of years that have elapsed. What would the value of t be here?